3. 6x + 8 = 12x + 4 x=-7: Thick Eyebrowsx = 2/3: Thin EyebrowsNo Solution: Thin eyelashesInfinite Solutions: Thick eyelashes

Amaya used 27 blue squares out of 36 carpet squares to cover the floor of her closet.

Given:

Amaya is using 36 carpet squares to cover the floor of her closet.

i.e. Total number of carpet squares Amaya used = 36

If 3/4 of the total carpet squares are blue is given.

So, assume blue squares = x

i.e 3/4 of total carpet squares = x

3/4 * 36 = x

Canceling by 4, We get,

=> x = 3 *9

=> x = 27

The value of x is equal to 27.

So, the value of other squares is equal to 1/4.

i.e 1/4 of total carpet squares = Other squares

1/4 * 36 = Other squares

Canceling by 4, We get,

=> Other squares = 9

The other square is 9.

Hence, she uses 27 blue squares to cover the floor of her closet.

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Step-by-step explanation:

we first square both sides to eliminate the square root brackets..

(√(m(y+n)/y)²= p²

m(y+n)/y = p²

(my +mn)/y =p²

so we multiply both sides by y to eliminate the denominator,

(my+mn)/y*y =p²*y

my+mn = p²y

collecting like terms,we have:

mn= p²y-my

so we seperate the y on the right hand side from the rest to have

mn = y(p²-m)

so divided both sides by the value in the bracket on the right hand side we have..

mn/(p²-m)=y(p²-m)/(p²-m)

so we have,

y= mn/(p²-m)

Answer:

y = \(\frac{-mn}{m-p^2}\)

Step-by-step explanation:

Given

\(\sqrt{\frac{m(y+n)}{y} }\) = p ( square both sides )

\(\frac{m(y+n)}{y}\) = p² ( multiply both sides by y )

m(y + n) = p²y ← distribute parenthesis on left side

my + mn = p²y  ( subtract p²y from both sides )

my - p²y + mn = 0 ( subtract mn from both sides )

my - p²y = - mn ← factor out y from each term on the left side

y(m - p²) = - mn ← divide both sides by (m - p²)

y = \(\frac{-mn}{m-p^2}\)

Answer:

Two dollars each

Step-by-step explanation:

Answer:

6/3 is 2. That's the total cost of each pencil.

Step-by-step explanation:  

Answer:

You did! well done

Step-by-step explanation:

Phil's monthly cost function: C(x) = 912, revenue function: R(x) = 464x, and profit function: P(x) = 464x - 912.

The fixed cost for owning the stand is given as $912 per month, which remains constant regardless of the number of rugs made and sold. Therefore, Phil's monthly cost function C(x) is simply the fixed cost: C(x) = 912.

The revenue generated from selling the rugs is dependent on the number of rugs made and sold each month. Since Phil earns $464 for each rug sold, his revenue function R(x) can be expressed as R(x) = 464x, where x represents the number of rugs made and sold.

To calculate Phil's profit, we subtract his total costs from his revenue. The profit function P(x) is given by P(x) = R(x) - C(x). Substituting the expressions for R(x) and C(x), we have P(x) = 464x - 912.

Therefore, Phil's monthly cost function is C(x) = 912, his revenue function is R(x) = 464x, and his profit function is P(x) = 464x - 912. These functions allow us to determine the cost, revenue, and profit associated with different quantities of rugs made and sold each month.

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Answer: 7/18

Step-by-step explanation:

Number of customers at Eva's boutique = 90

Number of customers who wore a size extra-large = 35

The probability that a randomly selected customer wore a size extra-large will be:

= Number of customers who wore a size extra-large / Number of customers at Eva's boutique

= 35 / 90

= 7/18

Therefore, the probability that a randomly selected customer wore a size extra large is 7/18.

Answer: total amount after 1 year will be 44759 + 4028.31 = 48,787.31

Step-by-step explanation:

SI = prt / 100

= 44759 x .09 x 1

= 4028.31

You have the following sequence given in the exercise:

You can identify that it is an Arithmetic sequence, because the difference between one term and the previous one is always the same:

By definition, you can express an Arithmetic sequence using a rule:

Where:

- The nth term of the sequence is

- The first term is

- The common difference is "d".

- The term position is "n".

In this case you know that:

Therefore, you can substitute this value into

Then, you get that the answer is:

The Binary Search Tree is as follows:

                                                   E

                                            /            \

                                         S                T

                                        /                    \

                                      I                       W

                                   /                            \

                                A                               M

                              /                                    \

                             C                                     G

                              \

                                D

The set of letters is {I, D, S, A, E, T, C, G, M, W} and len (I, D, S, A, a) = 5

Binary Search Tree:The binary search tree based on the alphabetical ordering of the letters is:

post-order sequence is: C, D, A, G, M, I, W, T, S, E.

To draw the binary search tree for the given post-order sequence, follow the steps below:

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Option (a) is correct: the t distribution with df = 1 is the most different from the standard normal distribution N(0,1).

The t-distribution with df = 1 is the most different from the standard normal distribution N(0,1).

The t-distribution is a family of distributions that is similar in shape to the normal distribution but has heavier tails. The degree of freedom (df) parameter determines the shape of the t-distribution. As the df increases, the t-distribution approaches the normal distribution.

When df = 1, the t-distribution has a very different shape from the normal distribution. It has a much higher peak and much heavier tails, making it a more extreme distribution than the normal distribution. This is because the t-distribution with df = 1 has less data to work with, which leads to more extreme values.

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Answer:

63

Step-by-step explanation:

9 x 14 = 126/2 = 63

The following equation could be used to represent a function w:

= w(x)=v(x-7)+7

According to the information provided,

The point of discontinuity of rational functions is at x=7.

When a rational function has a point of discontinuity, it generally occurs when,

q(x) = r(x-a), where x = a

In this case, we must pay attention to the following relationship, which is a combination of a parent rational function and a vertical translation:, (2)

If we know that a=7 and k=7.

The equation which can represent w is as follows,

w(x) = v ( x-7 ) + 7

A rational function can be represented as a polynomial split by another polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros in the denominator.

Example: x = f(x) (x - 3). The denominator, x = 3, has only one zero. Rational functions are no longer defined when the denominator is zero.

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The scale factor of the dilation of the given object is 4.

The scale factor of dilation:

The scale factor of the dilation of an object is determined by taking the ratio of image length to the corresponding object length.

Dilation is the process of resizing or transforming an object. The transformation that makes the objects smaller or larger with the help of the given scale factor.

The basic formula to find the scale factor of a dilated is:

Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

\(SD=\frac{32cm^2}{4cm^2}\)

SD=4

Thus, the scale factor of the dilation of the given object is 4.

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Answer:

ok im telling people to help u because i dont know that xd

Step-by-step explanation:

Answer:

90.29

Step-by-step explanation:

I did math

Answer:

8:31

Step-by-step explanation:

all of them are equal with 1:4 except 8:31

Answer:

5.66

Step-by-step explanation:

The sides of a square are equal. Let's call the length  

x

Use Pythagoras' Theorem.

Square the sides and add them together....

x

2

+

x

2

=

8

2

2

x

2

=

64

x

2

=

64

2

=

32

x

=

√

32

x

=

4

√

2

x

=

5.66

Answer:

2(m + 5)

Step-by-step explanation:

Twice means multiplication.

2 *

Sum means addition.

m + 5

2(m + 5)

Best of Luck!

The expected gestation period of this species with a 17-year life expectancy is approximately 430.2 days, rounded to one decimal place as needed.

A certain mammal has a life expectancy of about 17 years. To estimate the expected gestation period of this species, we can use the scatterplot provided, which shows Gestation Period (in days) vs. Life Expectancy (in years) for 18 species of mammals.

To determine if there is any evidence that an animal's gestation period is related to the animal's lifespan, we can look at the R-squared value provided, which is 86.5%. This indicates a strong positive correlation between gestation period and life expectancy.

To estimate the gestation period for the species with a 17-year life expectancy, we can use the provided linear regression equation:

Gestation = Constant + Coefficient * Life Expectancy

The given constant is 90.1808 and the coefficient is 20.

Gestation = 90.1808 + (20 * 17)

Gestation = 90.1808 + 340

Gestation ≈ 430.2 days

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Answer: 10 1/2 degrees Celsius

Step-by-step explanation:

The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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The angle of depression from the center of the Akashi Kaikyo Bridge to the platform is approximately 17.69 degrees, given a height of 297 meters and a length of 995 meters.



To determine the angle of depression from the center of the Akashi Kaikyo Bridge to the platform, we can use trigonometry. The angle of depression is the angle formed between a horizontal line and the line of sight from the observer to a point below them.

Let's consider a right-angled triangle, where the height of the platform (opposite side) is 297 meters and the length from the platform to the center of the bridge (adjacent side) is 995 meters. We want to find the angle of depression (θ).

Using the tangent function, we have:

tan(θ) = opposite/adjacent

tan(θ) = 297/995

To find θ, we can take the inverse tangent (arctan) of both sides:

θ = arctan(297/995)

Using a calculator, we find that arctan(297/995) ≈ 17.69 degrees.

Therefore, the angle of depression from the center of the bridge to the platform is approximately 17.69 degrees.

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0.403 is the probability that all three have a smart phone.

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Answer:

(8+2) + (8+2) + (8+2) + (8+2) + (8+2)

Step-by-step explanation:

The distributive property of multiplication allows you to show multiplication as addition.

Answer:

x ≤ 9

Step-by-step explanation:

4x – x + 8 ≤ 35

3x + 8 ≤ 35

3x ≤ 27

x ≤ 9

The circulation of the vector field F around the triangle is -324.

Stokes' theorem relates the circulation of a vector field around a closed curve to the curl of the vector field over the surface enclosed by the curve.

Therefore, to use Stokes' theorem to find the circulation of the vector field F = 6yi + 7zj + 6xk around the triangle obtained by tracing out the path from (4,0,0) to (4,0,6), to (4,3,6), and back to (4,0,0), we need to find the curl of F and the surface enclosed by the triangle.

The curl of F is given by:

curl F = ∇ x F

= (d/dx)i x (6yi + 7zj + 6xk) + (d/dy)j x (6yi + 7zj + 6xk) + (d/dz)k x (6yi + 7zj + 6xk)

= -6i + 6j + 7k

To find the surface enclosed by the triangle, we can take any surface whose boundary is the triangle.

One possible choice is the surface of the rectangular box whose bottom face is the triangle and whose top face is the plane z = 6.

The normal vector of the bottom face of the box is -xi, since the triangle is in the yz-plane, and the normal vector of the top face of the box is +zk. Therefore, the surface enclosed by the triangle is the union of the bottom face and the top face of the box, plus the four vertical faces of the box.

Applying Stokes' theorem, we have:

∮C F · dr = ∬S curl F · dS

where C is the boundary of the surface S, which is the triangle in this case.

Since the triangle lies in the plane x = 4, we can parameterize it as r(t) = (4, 3t, 6t) for 0 ≤ t ≤ 1.

Then, dr/dt = (0, 3, 6) and we have:

∮C F · dr = \(\int 0^1\) F(r(t)) · dr/dt dt

= \(\int 0^1\)(0, 18y, 42x) · (0, 3, 6) dt

=   \(\int 0^1\)378x dt

= 378/2

= 189.

On the other hand, the surface S has area 6 x 3 = 18, and its normal vector is +xi, since it points outward from the box.

Therefore, we have:

∬S curl F · dS = ∬S (-6i + 6j + 7k) · xi dA

\(= \int 0^6 ∫0^3 (-6i + 6j + 7k) .xi $ dy dx\)

\(= \int 0^6 \int 0^3 (-6x) dy dx\)

= -54 x 6

= -324

Thus, we have:

∮C F · dr = ∬S curl F · dS = -324.

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Stokes' theorem relates the circulation of a vector field around a closed path to the curl of the vector field over the surface bounded by that path. The circulation of the given vector field F around the given triangular path can be calculated as follows:

First, we find the curl of the vector field F:

curl(F) = ( ∂Fz/∂y - ∂Fy/∂z )i + ( ∂Fx/∂z - ∂Fz/∂x )j + ( ∂Fy/∂x - ∂Fx/∂y )k

= 6i + 7j + 6k

Next, we find the surface integral of the curl of F over the triangular surface bounded by the given path. The surface normal vector for this surface can be calculated as the cross product of the tangent vectors at two arbitrary points on the surface, say (4,0,0) and (4,0,6):

n = ( ∂r/∂u x ∂r/∂v ) / | ∂r/∂u x ∂r/∂v |

= (-6i + 0j + 4k) / 6

where r(u,v) = <4,0,u+v> is a parameterization of the surface.

Then, the surface integral of the curl of F over the triangular surface can be calculated as:

∫∫(S) curl(F) ⋅ dS = ∫∫(D) curl(F) ⋅ n dA

where D is the projection of the surface onto the xy-plane, which is a rectangle with vertices (4,0), (4,3), (4,6), and (4,0), and dA is the differential area element on D. The circulation of F around the given path is then given by:

∫(C) F ⋅ dr = ∫∫(D) curl(F) ⋅ n dA

= (6i + 7j + 6k) ⋅ (-i/6) (area of D)

= -19/2

Therefore, the circulation of the vector field F around the given triangular path is -19/2.

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We need to use the formula

PMT=P*i/(1-(1+i)^(-n))PMT

= payment P

= the principal amount (the initial amount you borrow or deposit)i

= the annual interest rate (5.5%)n

= the number of years the amount is deposited for;

since the investment makes payments at the end of each month for 10 years, n= 10*12=120 months

Therefore, PMT= 95,000*(0.055/4)/(1-(1+0.055/4)^(-120))= $819.96 (rounded to two decimal places) The size of each monthly payment is $819.96.b. Calculation of the principal portion of the 50th payment The principal portion of the 50th payment can be calculated using the following formula:P(50) = PMT*[(1 + i)^n - (1 + i)^(n - t)]/[(1 + i)^n - 1]Where n is the total number of payments, i is the interest rate per period, and t is the number of periods for which the payment has already been made. P(50) = $819.96*[(1 + 0.055/4)^120 - (1 + 0.055/4)^(120 - 50)]/[(1 + 0.055/4)^120 - 1]= $819.96*(4.8837 - 4.2874)/(4.8837 - 1)= $313.24 (rounded to two decimal places)

Answer: The principal portion of the 50th payment is $313.24.c. Calculation of the interest portion of the 60th payment The interest portion of the 60th payment can be calculated by subtracting the principal portion of the 60th payment from the total payment.P(60) = PMT*[(1 + i)^n - (1 + i)^(n - t)]/[(1 + i)^n - 1]P(60) = $819.96*[(1 + 0.055/4)^120 - (1 + 0.055/4)^(120 - 60)]/[(1 + 0.055/4)^120 - 1]= $819.96*(4.8837 - 3.1121)/(4.8837 - 1)= $464.80 (rounded to two decimal places)Interest Portion of 60th Payment = Total Payment - Principal Portion= $819.96 - $464.80= $355.16 The interest portion of the 60th payment is $355.16.

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Answer: 3

Step-by-step explanation:

test the numbers

Answer:

3

Step-by-step explanation:

first you divide the given number with 11 the remainder you get substract in order to get 0

Answer:

165000

Step-by-step explanation:

simple interest

PV(1+it)

150000(1+5*.02)

=165000

if you need it then the interest earned would just be 165000-150000= 15000

Based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

To solve the problem using the determinant method (Cramer's rule), we need to set up a system of equations based on the given information and then solve for the unknowns, which represent the number of 0.5 litre bottles and 0.7 litre bottles.

Let's denote the number of 0.5 litre bottles as x and the number of 0.7 litre bottles as y.

From the given information, we can set up the following equations:

Equation 1: 0.5x + 0.7y = 16.5 (total volume of moonshine)

Equation 2: 8x + 10y = 246 (total earnings from selling moonshine)

We now have a system of linear equations. To solve it using Cramer's rule, we'll find the determinants of various matrices.

Let's calculate the determinants:

D = determinant of the coefficient matrix

Dx = determinant of the matrix obtained by replacing the x column with the constants

Dy = determinant of the matrix obtained by replacing the y column with the constants

Using Cramer's rule, we can find the values of x and y:

x = Dx / D

y = Dy / D

Now, let's calculate the determinants:

D = (0.5)(10) - (0.7)(8) = -1.6

Dx = (16.5)(10) - (0.7)(246) = 150

Dy = (0.5)(246) - (16.5)(8) = -18

Finally, we can calculate the values of x and y:

x = Dx / D = 150 / (-1.6) = -93.75

y = Dy / D = -18 / (-1.6) = 11.25

However, it doesn't make sense to have negative quantities of bottles. So, we can round the values of x and y to the nearest whole number:

x ≈ -94 (rounded to -94)

y ≈ 11 (rounded to 11)

Therefore, based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

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Question

Matti is making moonshine in the woods behind his house. He’s selling the moonshine in two different sized bottles: 0.5 litres and 0.7 litres. The price he asks for a 0.5 litre bottle is 8€, for a 0.7 litre bottle 10€. The last patch of moonshine was 16.5 litres, all of which Matti sold. By doing that, he earned 246 euros. How many 0.5 litre bottles and how many 0.7 litre bottles were there? Solve the problem by using the determinant method (a.k.a. Cramer’s rule).