in the science club there are 2 sixth graders for every 3 seventh graders.

$866.25

1) Gathering the data

$1575

she spent 30%

she spent 3/14

2) Let's calculate it, starting with the 30% expense. Writing a factor, we have already the value:

1575 x ( 1 -0.3)

1575 x (0.7)

1102.50

Now let's proceed with the deduction of 3/14, which can be calculated through that:

1102.5 -3/14x (1102.5)

$866.25

3) Hence, Taylor's balance was after those payments of $866.25

Answer:

<DOE= 25

<AOE=145

<COB=90

BC=90

EA=145

ACE=235

Step-by-step explanation:

same thing as the last question :)

Answer:

The answer is b+17

Step-by-step explanation:

Answer:

12.56

Step-by-step explanation:

use the circumference of a circle formula, C=2πr, to find the circumference

so C=2π(2)=12.56 the last one

Answer:

66

Step-by-step explanation:

Find the area of the rectangle, then add up the area of the triangle.

The area of the rectangle

= 5 × 12

= 60 cm²

The base of the triangle

= 12 - 9

= 3 cm

The height of the triangle

= 9 - 5

= 4 cm

The area of the triangle

= (3 × 4) ÷ 2

= 6 cm²

The total area of the figure

= 60 + 6

= 66 cm²

The work done by force f in moving a particle counterclockwise around the given curve is zero.

The given force \(f = (x-5y)i + (5x-y)j\) is a conservative force. A conservative force is characterized by having a curl of zero, indicating that it can be derived from a potential function. For conservative forces, the work done over a closed path is always zero.

In this case, the particle moves counterclockwise around the circle defined by \((x-4)^2 + (y-4)^2 = 16\). Since the force f is conservative, the work done by f on the particle is independent of the path taken and depends only on the initial and final positions of the particle.

As the particle completes one counterclockwise revolution around the circle, it returns to its initial position. Therefore, the work done by force f is zero, indicating that the force does not transfer any energy to or from the particle.

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Answer:

2

Step-by-step explanation:

you find the gradient by doing y-y`/x-x`

so 3-9/-2-1 which gives you -6/-3 which is 2

The gradient of the straight-line that passes through the points, (-2, 3) and (1,9) is: 2.

Recall:

Given two points on a straight line as: (-2, 3) and (1,9)​

(-2, 3) = \((x_1, y_1)\)

(1, 9) = \((x_2, y_2)\)

Plug in the values into the slope/gradient formula

\(Gradient = \frac{9 - 3}{1 - (-2)} \\\\Gradient = \frac{6}{3}\\\\\mathbf{Gradient = 2}\)

Therefore, the gradient of the straight-line that passes through the points, (-2, 3) and (1,9) is: 2.

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The amount that the top class gets is $550

The amount that the second class gets is $250

The amount that the last class gets is $200

A fraction is non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 1/2.

Amount that each class get = (number of votes / total number of votes) x total amount divided

Amount that the top class gets = (275 / 500) x $1000 = $550

Amount that the second class gets = (125 / 500) x $1000 = $250

Amount that the last class gets = (100 / 500) x $1000 = $200

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Answer:

1100 bags, above is the solution to the question

Answer:A) 8 miles

Step-by-step explanation:

8 miles

Answer: 450

Step-by-step explanation:

almonds : raisins

4:3

600:?

600/4 = 150

3x150 = 450

there are 450 raisins in the bag.

Using the given ratio of almonds to raisins (4 to 3) and the number of almonds (600), a simple calculation using cross-multiplication leads to the conclusion that there are 450 raisins in the bag of trail mix.

Let's solve this problem using the concept of ratios. The question provides that the ratio of almonds to raisins in a bag of trail mix is 4 to 3. And we are also given that there are 600 almonds in the bag. Our task is to find out the number of raisins.

To do this, we can use cross-multiplication. It is a simple mathematical methodology to find an unknown value in a ratio. We will set up our equation as follows: 4/3 = 600/X.

Now, cross-multiply to find the value of X (raisins). The result is: X = (600*3) / 4 = 450.

So, there are 450 raisins in the bag.

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Answer:

We can determine that Option A, y = 0.4x - 2 is the correct answer

Step-by-step explanation:

Step 1:  Plug in 30 into the x-value to see if the y-value matches

Equation 1 --> y = 0.4(30) - 2 = 10

Equation 2 --> y = 0.3(30) + 2 = 11  <--  WRONG Y-VALUE

Equation 3 --> y = 0.3(30) + 1 = 10

Step 2:  Plug in 50 into the x-value to see if the y-value matches

Equation 1 --> y = 0.4(50) - 2 = 18

Equation 3 --> y = 0.3(50) - 2 = 13  <--  WRONG Y-VALUE

Answer: We can determine that Option A, y = 0.4x - 2 is the correct answer

The length of leg g given the length of leg f and angle G in the right triangle is 36.3 inches.

A right triangle is a 3 sided polygon that is made up of an hypotenuse. One of the angles measure 90 degrees.

G = Tan G x f

Tan 73 x 11

3.3 x 11 = 36.3 inches

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The unknown height of the student on the team, given the stem and leaf plot, would be 60 inches

To find the unknown height, we first have to list the heights of the known students on the team. From the stem and leaf plot, the heights are :

57, 59, 62, 65, 68, 70

The mean height of all the students is 63 inches which means that if this mean is denoted as x, the unknown height would be:

63  = ( 57 + 59 + 62 + 65 + 68 + 70 + x ) / 7

Solving for x gives:

7 x 63 = ( 381 + x )

441 = 381 + x

x = 441 - 381

x = 60 inches

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Answer:

Yes

Step-by-step explanation:

Reason: Both are congruent triangles by Side Angle Side congruent rule.

So, the flag will fit in the shadow box

The number of tractors lent by the first, second and third stations results in a system of three simultaneous equations which indicates;

The first originally station had 39 tractors, the second station had 21 tractors and the third station originally had 12 tractors

Simultaneous equations are a set of two or more equations that have common variables.

Let x represent the number of tractors at the first station, let y represent the number of tractors at the second tractor station, and let z, represent the number of tractors at the third tractor station

According to the details in the question, after the first transaction, we get

Number of tractors at the first station = x - y - z

Number of tractors at the second station = y + y = 2·y

Number of tractors at the third station = z + z = 2·z

After the second transaction, we get;

Number of tractors at the first station = 2·x - 2·y - 2·z

Number of tractors at the second station = 2·y - (x - y - z) - 2·z = 3·y - x - z

Number of tractors at the third station = 2·z + 2·z = 4·z

After the third transaction, we get;

Number of tractors at the first station = 2 × (2·x - 2·y - 2·z) = 4·x - 4·y - 4·z

Number of tractors at the second tractor station = 6·y - 2·x - 2·z

Number of tractors at the third tractor station = 4·z - (2·x - 2·y - 2·z) - (3·y - x - z) = 7·z - x - y

The three equations after the third transaction are therefore;
4·x - 4·y - 4·z = 24...(1)

6·y - 2·x - 2·z = 24...(2)

7·z - x - y = 24...(3)

Multiplying equation (2) by 2 and subtracting equation (1) from the result we get;

12·y - 4·x - 4·z - (4·x - 4·y - 4·z) = 16·y - 8·x = 48 - 24 = 24

16·y - 8·x = 24...(4)

Multiplying equation (3) by 2 and multiplying equation (2) by 7, then adding both results, we get;

14·z - 2·x - 2·y = 48

42·y - 14·x - 14·z = 168

42·y - 14·x - 14·z + (14·z - 2·x - 2·y) = 48 + 168

40·y - 16·x = 216...(5)

Multiplying equation (4) by 2 and then subtracting the result from equation (5), we get;

40·y - 16·x - (32·y - 16·x) = 216 - 48 = 168

8·y = 168

y = 168/8 = 21

The number of tractors initially at the second station, y = 21

16·y - 8·x = 24, therefore, 16 × 21 - 8·x = 24

8·x = 16 × 21 - 24 = 312

x = 312 ÷ 8 = 39

The number of tractors initially at the first station, x = 39

7·z - x - y = 24, therefore, 7·z - 39 - 21 = 24

7·z = 24 + 39 + 21 = 84

z = 84/7 = 12

The number of tractors initially at the third station, z = 12

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Answer:

B

Step-by-step explanation:

In the middle of the kite, there are 4 angles that are the same (90*)

So using the given angle 54 and the 90* we can find the last angle

54 + 90 = 144

180 - 144 = 36

The left-over angle is 36*

Answer:

l : y=4

m: 2x+y-4=0

n: x-y-1=0

p: x= -4

Answer:

Step-by-step explanation:

l:y=4

m:y=2x+4

n:y=x-1

p:x=-4

The expression cos(-θ)tan(-θ)csc(-θ) is equivalent to option (d) -1.

To find the equivalent expression, we can use the trigonometric identities:

cos(-θ) = cos(θ) [cosine is an even function]

tan(-θ) = -tan(θ) [tangent is an odd function]

csc(-θ) = -csc(θ) [cosecant is an odd function]

Substituting these identities into the expression, we get:

cos(θ) * (-tan(θ)) * (-csc(θ)) = cos(θ) * tan(θ) * csc(θ)

Since tan(θ) * csc(θ) = 1 (by the identity tan(θ) = sin(θ)/cos(θ)), the expression simplifies to: cos(θ) * 1 = cos(θ)

Therefore, the equivalent expression is -1.

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The proportionality constant from the original figure to the scaled copy is 2/9.

The constant of proportionality is the ratio between two given integers in what is known as a proportional relationship. The proportionality constant is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

We have here

To make a scaled duplicate, a four-sided figure is resized.

The proportionality constant from the original figure to the scaled copy is: 8/36 = 10/45 = 12/54 = 2/9.

As a result, the proportionality constant from the original figure to the scaled copy is 2/9.

Hence, the proportionality constant from the original figure to the scaled copy is 2/9.

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Answer:

The water level is rising because it is filling 10 more liters than it is draining

16.7 hours

Step-by-step explanation:

The rate at which the tank is filled and the rate at which the tank is draining

are constant.

Correct response;

Given:

Volume of water in the aquarium = 10,000 liters

Volume level at which the tank overflows = 12,000 liters

Level of the volume at which the fish get sick = 4,000 liters

Rate at which water enters the tank = 30 liter per minute

Rate at which the tank is draining the water = 20 liters per minute

Required;

The time it will take until the tank starts overflowing.

Solution:

Water that needs to be added to the tank before it begins to overflow = 12,000 liters - 10,000 liters = 2,000 liters

Let x represent the time after which the tank starts overflowing, the

(constant) rate of change function that gives the time it takes for the water

to overflow is therefore;

30·x - 20·x = 2,000

10·x = 2,000

x = 200 minutes = 3 hours and 20 minutes

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Answer:

did you use google.if not use it it is good to use.

For the answer of factors of expression (12 + 54), in the form of a(b + c), where a is the GCF of 12 and 54 is equals to 6( 2 + 9).

In math, to factor a number means to express it as a product of (other) whole numbers, called its factors. For example, if 7x5 = 35, 7 and 5 are both factors. The divisors that give the remainder to be 0 are the factors of the number. We have an expression of numbers, 12 + 54. We have to write this expression in form of a( b + c), where a is GCF of 12 and 54. Now, we can write the factors of 12 and 54 are 12 = 2×2×3

54 = 2×3 ×3×3

The greatest common factor, GCF of 12 and 54 is 2×3 = 6. So, 12 + 54 = 6× 2 + 6×9

Taking out the common factor 6 from above expression, 6( 2 + 9) which is required form a( b + c). Hence, required expression is 6( 2 + 9).

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Answer:

(1/4)n - 3

Step-by-step explanation:

In math, "of" means times so the first part of the expression is 1/4 times n. Then add minus 3 because it says she subtracted 3.

The solution of the given linear system of equations is x = 2, y = 1 and z = 2.

Given that the linear system of equations is

2x + 4y + 2z = 16-2x - 3y + z = -52x + 2y - 3z = -3

To solve the system of equations by Cramer's rule method, arrange them in the form of Ax = B as below:

A = [2, 4, 2; -2, -3, 1; 2, 2, -3], x = [x, y, z] and B = [16, -5, -3]

To find the inverse of the coefficient matrix A⁻¹, first, find the determinant of A as below:

|A| = 2[-3 - 2] - 4[-2 + 2] + 2[-8 + 1] = -12

The determinant is non-zero, hence A is invertible

A⁻¹ = 1/|A| [adj A]

where adj A is the transpose of the cofactor matrix [C] of A:

adj A = [C]T

So, we find [C] by replacing each element of A with its cofactor and taking its transpose matrix as below:

C = [5, 2, 6; 2, -2, 2; -4, -4, -4]

Then [C]T = [5, 2, -4; 2, -2, -4; 6, 2, -4]So, A⁻¹ = 1/|A| [adj A] = 1/(-12) [5, 2, -4; 2, -2, -4; 6, 2, -4] = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2]

To solve the system of equations, we have x = A⁻¹B as below:

x = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2][16; -5; -3] = [2; 1; 2]

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the side lengths of triangle AQRS are 8 cm, 6 cm, and 10 cm, and the side lengths of triangle AXYZ are 8 cm, 7 cm, and 10 cm.

The side lengths of triangle AQRS are:

AQ = 8 cm

QR = 6 cm

RS = 10 cm

The side lengths of triangle AXYZ are:

AX = 8 cm

XY = 7 cm

YZ = 10 cm

To find the side lengths of both triangles, we need to use the Pythagorean Theorem. For triangle AQRS, the hypotenuse is 10 cm, and the angle m2R is 55°. To find the other two side lengths, we need to use the formula a^2 + b^2 = c^2, where a and b are the side lengths and c is the hypotenuse. Since the hypotenuse is 10 cm, we can substitute c = 10 cm in the formula. We also know that the angle m2R is 55°. We can use the formula a/sin(m2R) = c/sin(90°) to solve for the length of side a. We can then substitute the length of side a in the formula a^2 + b^2 = c^2 to solve for side b. After finding the side lengths, we repeat the same steps to find the side lengths of triangle AXYZ. The hypotenuse is again 10 cm, and the angle m2Y is 35°. We can use the same formulas to solve for the other two side lengths. Therefore, the side lengths of triangle AQRS are 8 cm, 6 cm, and 10 cm, and the side lengths of triangle AXYZ are 8 cm, 7 cm, and 10 cm.

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Answer:

0.0567 x 10^4 < 2.3069 x 10^3 < 0.04069 x 10^5

Step-by-step explanation:

2.3069 x 10^5

4.069 x 10^5

0.567 x 10^5

Answer:

15-25

Step-by-step explanation:

The binomial expansion of (y - 3)⁴ is B) y⁴ - 12y³ + 54y² - 108y + 81.

The Binomial Theorem is the method of expanding an expression that has been raised to any finite power.

An expression of two terms having a degree n can be represented as,

(a - b)ⁿ = \(^nC_na^n - ^nC_{n-1}a^{n-1}b+^{n}C_{n-2}a^{n-2}b^2+...(-1)^n\times^nC_0a^0b^n\).

Given, (y - 3)⁴ = \(^4C_4y^4.3^0 - ^4C_3y^3.3 + ^4C_2y^23^2-^4C_1y.3^3+^4C_0y^03^4\).

(y - 3)⁴ = y⁴ - 12y³ + 54y² - 108y + 81.

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