Find parametric equations for an object moving clockwise along the ellipse (x²/9)+(y²/25)=1 beginning at (0,5) and requiring 3 seconds for a complete revolution.

x=
y=

Glens have 110 coins in his entire collection.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Glens coins from Denmark are eleven 11.

These 11 coins are 10% of his entire coins.

We need to find how many coins Glens has.

Let x be the entire collection of Glens coins

10/100x=11

0.1x=11

Divide both sides by 0.1

x=110

Hence, Glens have 110 coins in his entire collection.

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Answer:

10 cm

Step-by-step explanation:

since DE is probably equal to AD which is 17 we subtract the length of the side of CD to find CE

Length CD can be found because it is equal to AB which is 7 cm so we subtract

17-7=10

Hopes this helps please mark brainliest

Answer:

CE = 10

Step-by-step explanation:

Because they are congruent:

AD = 17, that means DE = 17

AB = 7, that means CD = 7

To find what CE is, we start with the full length:

DE

and by subtracting CD (that's part of the length), we can get CE.

DE - CD = CE

Just substitute the values in:

17 - 7 = 10

CE = 10

So there's the answer, but check this out:

CE + CD = DE

10 + 7 = 17

The monthly payment on the amortized loan is $206.74. The car cost in total is $14, 885. 52. The money paid in interest is $1, 861.52.

The monthly payment is called an annuity because it is constant and remains the same.

Use the present value of an annuity to find the monthly payment to be:

Loan amount = Monthly payment x Present value interest factor of annuity, period, rate

The period is:
= 6 years x 12

= 72 months

The rate is:

= 4.5% / 12 months a year

= 0.375%

The loan amount is:

= 14, 800 x ( 1 - downpayment)

= 14, 800 x ( 1 - 12%)

= $13, 024

The monthly payment is:

13, 024 = Monthly payment x Present value interest factor of annuity, 72 periods , 0.375%

Monthly payment = 13, 024 / 62.995976235992

= $206.74

The car cost in total is:

= Monthly payment x Number of months

= 206. 74 x 72

= $14, 885. 52

The money paid in interest is:

= Loan amount - Car cost

= 14, 885.52 - 13, 024

= $1, 861.52

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As per the given matrix A and B, the value of -7A - 6B is [tex]-7A - 6B = \begin{bmatrix} 40 & -106 &-32 \\ -46& 43 &25 \\82 & -62& -22 \end{bmatrix}[/tex]

Matrix:

Basically, a set of numbers arranged in rows and columns so as to form a rectangular array is known as matrix.

Given,

Here we have the matrix A and B.

Now we have to find the -7A - 6B.

In order to solve this matrix, first we have to find the value of -7A,

To find that one, we have to multiply -7 with A,

Then we get,

[tex]-7 \times\begin{bmatrix}-10 &10 &8 \\ -2& -1 &5 \\ -4& 8& -6\end{bmatrix} = \begin{bmatrix}70 &-70 &-56 \\ 14& 7 &-35 \\ 28& -56& 42\end{bmatrix}[/tex]

Similarly, we have to find the value of 6b,

In order to find that, we have to multiply 6 with the matrix B,

Then we get,

[tex]6 \times\begin{bmatrix}5 &6 &-4 \\ 10& -6 &-10 \\ -9& 1& 10\end{bmatrix} = \begin{bmatrix}30 & 36 &-24 \\ 60& -36 &-60 \\ -54& 6& 60\end{bmatrix}[/tex]

Now, we have to subtract the resulting matrix,

[tex]-7A - 6B = \begin{bmatrix}70 &-70 &-56 \\ 14& 7 &-35 \\ 28& -56& 42\end{bmatrix} - \begin{bmatrix} 30 & 36 &-24 \\ 60& -36 &-60 \\ -54& 6& 60 \end{bmatrix}[/tex]

Therefore, the resulting matrix is

[tex]-7A - 6B = \begin{bmatrix} 40 & -106 &-32 \\ -46& 43 &25 \\82 & -62& -22 \end{bmatrix}[/tex]

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Answer:

50 degrees

Step-by-step explanation:

sum of all three angles on any triangle is equal 180 degrees so first we add the first 2 given angles

70+60

130

Now we subtract from 180 to find the unknown angle

180-130

50 degrees

Hopes this helps please mark brainliest

x + 60° + 70 = 180°

( sum of interior angle of triangle is 180° )

x + 130° = 180°

x = 180° - 130°

x = 50°

hope it helps...

The equation that can be used  to determine the number of plates p, that he used is 6p = 48.

Jim is a preschool teacher. While he was getting ready for his class's snack time, he put 6 carrots on each plate.

He used 48 total carrots. The equation that could be used to determine the number of plates, p, that he used can be represented as follows:

let

p = number of of plates

Therefore,

6 carrots are put on each plate.

He has 48 carrots.

Hence, the equation is  6p = 48

p = 48 / 6

p = 8

Therefore,

number of plates = 8

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The number of plates he used is can be calculated by 6p = 48

How to determine this?

He was said to put 6 carrots on each plates

And used 48 total carrots  altogether

p representing the number of plates

That is, 6 carrots in p places

6 carrots × p

= 6p

Given that 48 carrots used altogether

6p = the total number of carrots

Therefore, 6p  = 48

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Answer:

Step-by-step explanation:

2x+3x+8-3x-2 = 2x + 6

The probability that a student chosen at random is in the choir or band or both is 0.911

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In mathematics terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6. One is an event that will happen, it is certain.

Total number of students in the school = 450

number of students in choir = 110

number of students in band = 240

number of students in both = 60

Probability a student chosen at random is in the choir or band or both is

110/450 + 60/450 + 240/450

= 410/450 which is 0.911

In conclusion, the probability of a student being in music, or band or both is 0.911

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The solution for implicit differentiation is

[tex]\frac{d^{2}y }{dx^{2} } =-\frac{16}{25y^{3} }[/tex]

What is implicit differentiation?

In mathematics, differentiation is the process of determining the derivative, or rate of change, of a function. Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure that determines the instantaneous rate of change of a function based on one of its variables. The process of finding the derivative of dependent variable in an implicit function by differentiating each term separately

Given data ,

Let the function be [tex]4x^{2} -5y^{2} =4[/tex]   be equation (1)

Now , on differentiating the terms with respect to y , we get

[tex]4x^{2} -5y^{2} =4[/tex]

[tex]8x-10y\frac{dy}{dx} = 0[/tex]

[tex]8x=10y\frac{dy}{dx}[/tex]

[tex]\frac{dy}{dx}=\frac{4}{5} \frac{x}{y}[/tex]   be equation (2)

So , the first derivative is [tex]\frac{dy}{dx}=\frac{4}{5} \frac{x}{y}[/tex]

Now , on taking the derivative of equation (2) , we get

[tex]\frac{d^{2} y}{dx^{2} } =\frac{4}{5}(\frac{y-x\frac{dy}{dx} }{y^{2} } )[/tex]

Substituting the value for dy/dx from equation (1) , we get

[tex]\frac{d^{2} y}{dx^{2} } =\frac{4}{5}(\frac{y-x\frac{4}{5}\frac{x}{y} }{y^{2} } )[/tex]

On simplifying the equation , we get

[tex]\frac{d^{2} y}{dx^{2} } =\frac{4}{5} ( \frac{5y^{2}-4x^{2} }{5y^{3} } )[/tex]    be equation (3)

Substituting the value for 5y² - 4x² = -4 from equation (1) we get

[tex]\frac{d^{2} y}{dx^{2} } =\frac{4}{5} ( \frac{-4 }{5y^{3} } )[/tex]

So , the implicit differentiation value is

[tex]\frac{d^{2} y}{dx^{2} } =\frac{-16}{25y^{3} }[/tex]

Hence , The solution for implicit differentiation is

[tex]\frac{d^{2}y }{dx^{2} } =-\frac{16}{25y^{3} }[/tex]

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The scientific notation of 69200000 is  6.92 × 10⁷

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.

Scientific Notation is a special way of writing numbers:

For example 800 is written as 8 × 10² in Scientific Notation.

Therefore, let's write the scientific notation of the number 69200000.

Hence,

69, 200, 000 = 6.92 × 10⁷

The logic is that we will count backwards until we meet the last number.

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The percentage of confidence intervals that would capture the true population means is approximately 95% of them. which is the correct answer would be option (C).

There were 100 random samples of the same size drawn from a population known to have a normal distribution with a mean and a standard deviation.

For each of the 100 random samples, a 95% confidence interval for the population mean was created.

Since all the conditions are satisfied,

Therefore, the percentage of confidence intervals that would capture the true population means is approximately 95% of them.

Hence, the correct answer would be an option (C).

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Answer:

[tex]2(w-6^2)[/tex]

Step-by-step explanation:

We are doubling the difference, so we first need to find the difference. Our two numbers are [tex]w[/tex] and [tex]6^2[/tex] (you can also write 36 but that is how the problem states it). Therefore, the equation for that is [tex]w-6^2[/tex]. Then, if we double it, we get [tex]2(w-6^2)[/tex].

The Perimeter of the given Reactangle is 6*length

Whta is a Rectanglee?

A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. It can alternatively be classified as an equiangular quadrilateral since all of its angles are equal; or a parallelogram with a right angle. A square is a rectangle with four equal-length sides.

Solution:

Let,

the length be l

and breadth be b

According to the question,

l = (1/2)b

We know that Perimeter of Rectangle = 2(length + breadth)

From the variable mentioned above

Perimeter = 2*(l+b)

Perimeter = 2*(l + 2l)

Perimeter = 2*(3l)

Perimeter = 6l

The Perimeter of the given Reactangle is 6*length

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Answer:

Let x be the width of the rectangle.

The expression to represent the perimeter of the rectangle is 3x.

Step-by-step explanation:

Definition of the variable:

If the rectangle has a length that is half its width, then:

The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, the perimeter of a rectangle is twice the sum of its length and width.

[tex]\begin{aligned}\textsf{Perimeter of the rectangle}&=2 \left(\;\sf length+width\; \right)\\& = 2\left(\dfrac{1}{2}x+x\right)\\& = 2 \left(\dfrac{3}{2}x\right)\\& = 3x\end{aligned}[/tex]

Therefore, an expression to represent the perimeter of the rectangle is:

The nth term of the sequence is aₙ = 48 + 2n

The definition of the function is given as

a₁= 50

aₙ = aₙ₋₁ + 2

The above definitions imply that we simply add 2 to the previous term to get the current term

Using the above as a guide, we have:

The common difference, d = 2

First term, a = 50

The nth term of the sequence is calculated as

aₙ = a₁ + (n - 1)* d

Substitute the known values in the above equation

So, we have the following representation

aₙ = 50 + (n - 1)* 2

So, we have

aₙ = 50 + 2n - 2

Evaluate the like terms

aₙ = 48 + 2n

Hence, the nth term is aₙ = 48 + 2n

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If we use more than 133 minutes then the 2nd plan will be preferable.

Given:

The first plan charges a rate of 26 cents per minute. The second plan charges charges a monthly fee of $19.95 plus 11 cents per minute.

26 cents = $0.26

Let m be the minutes

19.95 + .17m < .32m

Subtract .17m from both sides

19.95 < .32m - .17m

19.95 < .15m

Divide both sides by .15

19.95/.15 < m

133 < m

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The value obtained after solving the expression will be equal to (-1, 1).

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both.

Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given in for the mention in the question,

x² = 36

x = ±6

Therefore, the values are -6, and +6.

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Answer:

-35/-7=5

Step-by-step explanation:

Diviser par de nombre négatif alors sa devient positif pareil pour la multiplication

Step-by-step explanation:

Zhang invests $2,600 in two different accounts. The first account paid 11%, the second account paid 5% in interest. At the end of the first year he had earned $220 in interest. How much was in each account?

11% = 0.11

in account 1: $220/0.11 = $2,000

in account 2: $2,600 - $2,000 = $600

$2,000 At 11%

$600 At 5%

The fraction of the given is 1/7 .

What is fraction?

 A fraction that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Here let us take x as numerator and y as denominator. Then

If the numerator is multiplied by 3 and denominator is reduced by 2, we get 3/5 ,

=> 3x/y-2 = 3/5

=> 5*3x =3(y-2)

=> 15x=3y-6

=> 5x=y-2

=> y =5x+2------>1

Now if the numerator is increase by 4 and the denominator is double we get 5/14,

=> (x+4)/2y = 5/14

=> 14x+56 = 10y

=> 7x+28=5y ---->2

Here put 1 into 2 then,

=> 7x+28 = 5(5x+2)

=> 7x+28=25x+10

=>18x=18

=> x =1

Now put x=1 into 1 then,

=> y =5(1)+2 = 7.

Therefore the given fraction is x/ y = 1/7.

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The smallest number is 5, middle number is 8 and largest number is 11.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let x be the smallest number.

let x + 3 be the middle number.

let x + 6 be the largest number.

Then, the equation is

5 (x + 6) = 3 x + 5 (x + 3)

5x+ 30 = 3x+ 5x + 15

3x = 30- 15

3x= 15

x= 5

So, the numbers are x = 5, x + 3 = 8, and x + 6 = 11.

Now, the difference between each succeeding number is 3.

5 x 11 = 55

3 x5 + 5 x 8 = 15 + 40 = 55

Hence, the smallest number is 5, middle number is 8 and largest number is 11.

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Answer:

Lauren has 30 jellybeans

Step-by-step explanation:

Let x - Lauren

Let y = Haley

[tex]\frac{x}{y}[/tex] = [tex]\frac{3}{8}[/tex]  Cross multiply

8x + 3y

x = y - 50  Substitute y - 50 into the equation above for x

8(y -50) = 3y

8y -400 = 3y  Subtract 8y from both sides

-400 = -5y  Divide both sides by -5

80 = y  This is Haley's jellybeans

x = y = 50

x = 80 - 50

x = 30 This is Lauren's jellybeans.

The corresponding probabilities of the random variables x = (0, 1, 2, 3, 4, 5, and 6) are  (0.2401, 0.4116, 0.2646, 0.0756, 0.0081, 0, and 0)

Since we are dealing with a binomial probability distribution. We are going to use the binomial distribution formula for determining the probability of x successes:

P(x = r) = nCr . π^r  . q^n-r

Given: n = 4 and π = 0.30, q = 1 - π = 1 - 0.30 = 0.70 and x = (0, 1, 2, 3, 4, 5, 6)

P(x = 0) = 4C0 × 0.3⁰ × 0.7⁴⁻⁰ = 0.2401

P(x = 1) = 4C1 × 0.3¹ × 0.7⁴⁻¹ = 0.4116

P(x = 2) = 4C2 × 0.3² × 0.7⁴⁻² = 0.2646

P(x = 3) = 4C3 × 0.3³ × 0.7⁴⁻³ = 0.0756

P(x = 4) = 4C4 × 0.3⁴ × 0.7⁴⁻⁴ = 0.0081

P(x = 5) = 0

P(x = 6) = 0

Note: P(x = 5) and P(x = 6) are 0 because their x (5 and 6) is greater than the n (4)

Therefore, the probabilities of the random variables x(0, 1, 2, 3, 4, 5, and 6) are  0.2401, 0.4116, 0.2646, 0.0756, 0.0081, 0, and 0 respectively

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Answer:

a) Total preferred dividend = $37,020; total common stock dividend = $26,980.

b) Total preferred dividend = $12,340; total common stock dividend = $51,660.

C) see explanation section.

Explanation:

Requirement - A

If the preferred dividend is cumulative.

Common stock = $12 x 50,000 = $600,000

Preferred stock = $19.5 x 7,910 = $154,245

Given,

Retained Earnings = $240,000, and Dividend = $64,000.

Generally, cash dividend is distributed to the preferred and common stockholders. However, after paying the preferred stock, dividend is paid to the common stockholders.

Therefore, preferred dividend = $154,245 x 8% = $12,340 for 2019.

As the preferred dividend is cumulative, the preferred stockholders will get the dividend for 2017 and 2018 if there remains any extra dividend after giving for 2019.

For 2017 = $12,340

For 2018 = $12,340

For 2019 = $12,340

Total preferred dividend = $37,020.

Therefore, the total common stock dividend = $(64,000 - 37,020) = $26,980.

Requirement - B

If the preferred dividend is non-cumulative.

Therefore, preferred dividend = $154,245 x 8% = $12,340 for 2019.

As the preferred dividend is non-cumulative, the preferred stockholders will not get the dividend for 2017 and 2018 despite remaining extra dividend after providing for 2019.

Therefore, preferred dividend = $12,340

Common stock dividend = $(64,000 - 12,340) = $51,660.

Requirement - C

The common stock dividend is more in non-cumulative as the company does not pay the previous years' dividends to the preferred dividend. On the other hand, if the company pays the dividend for the last years', which is known as cumulative, the dividend will become less. Therefore, the common stockholders will get fewer dividends because of paying the previous years' dividend to the preferred stockholders.

The factors would cause a more favorable dividend for the common stockholders if preferred dividends were non-cumulative, not in arrears, and there is an increase of distribution of dividends.

If all the television at the stores are 3/4 of the original price and has a $40 discount coupon, then the equation which she used to find the price of the television is f = (3/4)p - 40

The original price of the television = p

The 3/4 of the original price = (3/4)p

The worth of the discount coupon = $40

So the discount price will be subtracted

Then, the final price of the television = (3/4) × The original price of the television - The worth of the discount coupon

Substitute the values in the equation

The final price of the television f = (3/4)p - 40

Hence, If all the television at the stores are 3/4 of the original price and has a $40 discount coupon, then the equation which she used to find the price of the television is f= (3/4)p - 40

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Answer: x = -8

Step-by-step explanation:

1. Add 10 to both sides

-3x = 14 + 10

2. Simplify 14 + 10 to 24

-3x = 24

3. Divide both sides by -3

x = [tex]-\frac{24}{3}[/tex]

4. Simplify [tex]\frac{24}{3}[/tex] to 8

x = -8

The value of p is 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

Given that

Point A(p8,4p+5) is located on a line that connects M(-2,-5) and N(1,-10).

The equation of line that passing through points  M and N,

Use the formula of equation of line,

y-y₁ = (y₂-y₁/x₂-x₁)(x-x₁)

y-(-5) = (-10+5/1+2)(x-(-2))

⇒ y+5 = -5/3(x+2)

⇒5x+3y +25 = 0    (1)

Since, line passes through point  A(p−8,4p+5), so this point A will satisfy the equation (1)

5(p-8)+3(4p+5)+25 = 0

⇒ 17p = 0

⇒ p = 0

The value of p is 0.

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The relation for x and y is given as y = 26/x. The correct answer is option (B).

When two quantities have some dependence in their values they can be said proportional to each other.

It can be of two types such as direct and indirect.

The direct proportionality means the values of both the quantities are increasing or decreasing at the same time while the indirect proportionality implies value of one quantity is increasing while the other is decreasing.

Given that,

The proportionality relation between x and y as

y ∝ 1/x

And, y = 2 at x = 13.

Suppose k is the constant of proportionality.

Then, y = k/x

Substitute y = 2 and x = 13 in the above equation to obtain,

2 = k/13

=> k = 26

Thus, by substituting the value of k the equation can be written as y = 26/x.

Hence, the equation that relates x and y is y = 26/x.

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