Evaluate:
Σ21(2n + 8) = [?]
HELP ME PLS

The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say that number is x,

Quotients of 20 and x will be given as 20/x

20/x - 4 = 0

20/x = 4

x = 20/4 = 5

Hence"The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5".

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The quantity of salt in the tank at time t is given by Q(t) = 640 (1 - e^(-t/40)) for 0 ≤ t ≤ 90.

To solve this problem, we need to use a differential equation to model the rate of change of the quantity of salt in the tank. Let Q(t) be the quantity of salt in the tank at time t.

Then, the rate of change of Q is given by:

dQ/dt = (rate of salt in) - (rate of salt out)

The rate of salt in is given by the concentration of salt in the incoming water, multiplied by the rate at which water is added to the tank:

rate of salt in = c * 2

The rate of salt out is given by the concentration of salt in the solution in the tank, multiplied by the rate at which water is leaving the tank:

rate of salt out = (Q(t) / (160 + 2t)) * 1

Putting these together, we get the following differential equation:

dQ/dt = 2c - (Q(t) / (160 + 2t))

To solve this differential equation, we can use separation of variables. Rearranging the equation, we get:

(160 + 2t) dQ/dt + Q(t) = 2c(160 + 2t)

Multiplying both sides by the integrating factor e^(2t/160), we get:

d/dt (e^(2t/160) Q(t)) = 2c e^(2t/160)

Integrating both sides with respect to t, we get:

e^(2t/160) Q(t) - Q(0) = 160c (e^(2t/160) - 1)

Solving for Q(t), we get:

Q(t) = Q(0) e^(-2t/160) + 160c (1 - e^(-2t/160))

Substituting Q(0) = 0, since there is no salt initially in the tank, we get:

Q(t) = 160c (1 - e^(-2t/160))

Finally, we can substitute c = 4, since the concentration of salt in the incoming water is 4 pounds per gallon.

Thus, the quantity of salt in the tank at time t is:

Q(t) = 640 (1 - e^(-t/40))

We can now use this formula to find Q(t) for 0 ≤ t ≤ 90:

Q(0) = 0

Q(90) = 640 (1 - e^(-90/40)) ≈ 908.22 pounds

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C, D, and E would all be Statistical Questions.

Answer:

(2x-1)(x+3)

Step-by-step explanation:

2x(x+3)-1(x+3)

(2x-1)(x+3)

Answer:

(x + 1) (2 x + 3)

Step-by-step explanation:

Write the middle term as + 5 x = 2 x + 3 x

And factor by grouping:

2 x^2 + 2 x + 3 x - 3

2 x (x + 1) + 3 (x + 1)

(x + 1) (2 x + 3)

I do not understand what do you mean

The analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.

It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.

As we have given about the Euclidean and analytical geometry.

Without using any numerical measurements, we have investigated the connections between points, lines, and planes in Euclidean geometry.

In analytical geometry, we've looked at how the locations of points in a Cartesian coordinate system related to algebra and geometry.

The analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.

If the Euclidean geometry can be more advantageous in particular circumstances

Example: If using terrain or building chart),

Thus, the analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.

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The perimeter of a triangle is equal to the sum of all the sides of the triangle.

A triangle has 3 sides so:

Perimeter = side 1 + side 2+ side 3

We have the values of the perimeter and two sides:

perimeter = 30x + 40

Side 1= 12x + 6

Side 2= 10x + 20

S3= ?

So, replacing with the values given:

30x+40= (12x+6)+(10x+20)+ S3

Solving for S3 ( side 3)

30x+40= 12x+6+10x+20+S3

30x+40=12x+10x+6+20+S3

30x+40= 22x+26+S3

30x+40-22x-26=S3

30x-22x+40-26=S3

8x+14 =S3

Lenght of the third side = 8x+14

Answer:

2?

Step-by-step explanation:

Answer:

102

Step-by-step explanation:

34 is d so 34×3=102

pls correct me if im wrong

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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There will be two x-intercept for the quadratic function

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution.

The value of y in the quadratic equation ax²+bx+c=0 is y ≤ 2. This means that the maximum value is 2.

With this that the parabola will be downward and and the maximum value will be 2.

With this there will be two intercepts on the x axis.

Therefore for a range of y≤2 there will be two x-intercept.

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Answer:

A.Because it looks like a deal

Step-by-step explanation:

17$ a day for 30 days is just multiplication which ends up with 510$ which is the full price they only put the ad up to make it seem like a deal. Understand well il break it down for you take the seventeen and 30. multiply the 7 and the 30 then 10 and the 30. add both of the products together to get 510 or 510$.

Answer:

3.5 in²

Step-by-step explanation:

Given:

Radius (r) = 1.5 in.

Formula for area of half circle = (πr²)/2

Required:

Area of the half circle

Solution:

Plug in the values into the formula for area of half circle.

Thus:

Area = (π × 1.5²)2

= 7.06858347/2

Area = 3.5 in² (nearest tenth)

The operation that has been performed on v to result in the vector that is shown is multiplication by -1.

The vector that is shown is (-2, -1). This can be obtained from vector v = (2, 1) by multiplying it by -1. Multiplying a vector by a negative number reverses its direction.

Multiplication of a vector by a number is performed component-wise. This means that each component of the vector is multiplied by the number. In the case of (-1) * (2, 1), each component is multiplied by -1. This results in the vector (-2, -1).

Here is the mathematical equation:

(-1) * (2, 1) = (-2, -1)

Therefore, the operation that has been performed on v to result in the vector that is shown is multiplication by -1.

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Answer:

(4,4)

Step-by-step explanation:

1) Using substitution: move 7y to the other side by subtraction

x = 32 - 7y

2) substitute in for x in the first equation

-2(32 - 7y) + 7y = 20

3) distribute

-64 + 14y + 7y = 20

4) add like terms and solve for y

21y = 84

y = 4

5) plug in y value of for in one of the eqautions to get x value

-2x + 7(4) = 20

x = 4

Answer:

5/6+1/8 = 23/24

Step-by-step explanation:

The lowest common denominator here is the smallest denominator that can be divided evenly by both 6 and 8.  It is 24.  Note that 6 = 2·3 and that 8 = 2·2².  We use the factors 2³ and 3 to come up with the LCD 24.

Then 5/6 + 1/8 can be rewritten with this LCD as:

20/24 + 3/24 = 23/24

5/6+1/8 = 23/24

Answer:

B & D

Step-by-step explanation:

Volume is calculated as:

\(Volume = Length * Width * Height\)

For (a):

\(Length = 3cm\)

\(Width = 4cm\)

\(Height = 5cm\)

\(Volume = 3cm * 4cm * 5cm\)

\(Volume = 60cm^3\)

For (b):

\(Length = 3cm\)

\(Width = 4cm\)

\(Height = 3cm\)

\(Volume = 3cm * 4cm * 3cm\)

\(Volume = 36cm^3\)

For (c):

\(Length = 4cm\)

\(Width = 2cm\)

\(Height = 2cm\)

\(Volume = 4cm * 2cm * 2cm\)

\(Volume = 16cm^3\)

For (d):

\(Length = 2cm\)

\(Width = 3cm\)

\(Height = 6cm\)

\(Volume = 2cm * 3cm * 6cm\)

\(Volume = 36cm^3\)

There's no need to check for (e)

Option b and d answers the question

Using the volume of a rectangular prism to examine the volumes of the prism, the two prisms with a volume of 36cm³ are B and D

Recall :

Prism A :

Volume = 3cm × 5cm × 4cm = 60 cm³

Prism B :

Volume = 3cm × 3cm × 4cm = 36 cm³

Prism C :

Volume = 4cm × 3cm × 2cm = 24 cm³

Prism D :

Volume = 2cm × 6cm × 3cm = 36 cm³

Prism E :

Volume = 4cm × 2cm × 2cm = 16 cm³

Hence, the two rectangular prisms with a volume of 36cm³ are B and D.

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Answer:

Step-by-step explanation:

    A,  use  three_digite  rounding  arithmetic  to compute  13- 6 and determine  the absolute,relative ,and percentage errors.

tepeat part (b) using  three – digit chopping arithmetic.

9514 1404 393

Answer:

  A = 2000(1 +1)^(t/9)

  $64,000

Step-by-step explanation:

The growth rate is 100% in 9 years, so the equation can be written ...

  A = 2000(1 +1.00)^(t/9)

The amount in 45 years is ...

  A = 2000(2^5) = 2000×32 = 64,000 . . . dollars

Answer:

\(m=\frac{-1}{3}\)

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Simply plug in the 2 coordinates into the slope formula to find slope m:

(-1, -1)

(2, -2)

\(m=\frac{-2-(-1)}{2-(-1)}\)

\(m=\frac{-2+1}{2+1}\)

\(m=\frac{-1}{3}\)

To Write :

\(y = 6x^2 + 18x + 14\) in the form \(y = a(x -h)^2 + k\) ?

Solution :

\(y = 6x^2 + 18x + 14\\\\y = (\sqrt3 x)^2+(2\times \sqrt{3}\times 3\sqrt{3} )x +(3 \sqrt{3} )^2- (3 \sqrt{3} )^2+14=0\\\\y = ( \sqrt{3}x+ 3\sqrt{3})^2+14-27 =0\\\\y = ( \sqrt{3}x+ 3\sqrt{3})^2 - 13 =0\\\\y= 3(x + 3)^2-13=0\)

Therefore, this is the simplified form.

you can start by dividing the total length of the road by the distance that can be repaired per week:

13 km ÷ 3 1/2 km/week = 3.71 weeks

Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.

The solution is

The number of small boxes shipped = 6 boxes

The number of large boxes shipped = 12 boxes

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

Let the number of small boxes be = x

There were twice as many large boxes shipped as small boxes shipped

So ,

Let the number of large boxes be = 2x

The area of small box = 9 feet³

The area of large box = 17 feet³

The total area of the boxes shipped = 258 feet³

Now , the equation will be

Area of small box x number of small boxes + area of large box x number of large boxes = total area of the boxes shipped

Substituting the values in the equation , we get

9x + 17 ( 2x ) = 258

9x + 34x = 258

On simplifying the equations , we get

43x = 258

Divide by 43 on both sides of the equations , we get

x = 6

Therefore , the number of small boxes = 6

The number of large boxes = 2x = 12 boxes

Hence ,

The number of small boxes is 6 and the number of large boxes is 12

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Answer:

1/4

Step-by-step explanation:

First you add all of the marbles in the bag which is 16 marbles.  The fraction of red marbles to the total would be 4/16.  In the simplest form that is 1/4. You can also just do 4 divide by 16 which gives you 0.25 and in decimal form that is 1/4.

Using word problems and equations, Sarah worked for 10 hours and Penelope worked for 5 hours

This is a word problem and in order to solve this, we need to translate mathematical statements in form of word problems into mathematical equations.

Let's assume that Sarah worked x hours.

Given that Sarah can iron 30 shirts per hour, the total number of shirts she ironed is 30x.

Since Penelope worked half the hours of Sarah, Penelope worked x/2 hours.

Given that Penelope can iron 35 shirts per hour, the total number of shirts she ironed is 35 * (x/2) = (35/2)x.

The total number of shirts ironed by both Sarah and Penelope is 475 shirts.

So, we can write the equation: 30x + (35/2)x = 475.

To solve this equation, we can simplify it: (60/2)x + (35/2)x = 475, which becomes (95/2)x = 475.

Now, we can solve for x: x = (475 * 2) / 95 = 10.

Therefore, Sarah worked 10 hours and Penelope worked half of that, which is 5 hours.

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Answer:

42.6 ft

Step-by-step explanation:

1 - 4/5 = 5/5 - 4/5 = 1/5

Since 4/5 of the roll was used, 1/5 of the roll is left.

1/5 * 213 ft = 213/5 ft = 42.6 ft

Step-by-step explanation:

Identity the variable:

Initial Velocity is 35.

Initial Height is 204

Final Height is 0.

What looking for the time.

So we have

\(0 = - 16 {t}^{2} + (35)t + 204\)

Use Quadratic Formula,

\( - b± \frac{ \sqrt{b {}^{2} - 4ac} }{2a} \)

A is -16, B is 35 , C is 204.

So we have

\( - 35± \frac{ \sqrt{ {35}^{2} - 4( - 16)(204) } }{ - 32} \)

\( - 35± \frac{ \sqrt{1225 + 2240} }{ - 32} \)

\( - 35± \frac{ \sqrt{3465} }{ - 32} \)

\({35} ± \frac{ \sqrt{3465} }{ - 32} \)

The positve solution is

\(4.83\)

So the answer is 4.83 seconds

The steady-state probabilities of the cars being in City A and City B are both 0.667.

How to solve a Matrix?

(a) The stochastic matrix M describing the movement of cars between City A and City B can be written as:

M = [ 0.8  0.1 ]

     [ 0.2  0.9 ]

The entry in row i and column j represents the probability of a car that was in City j being in City i the next day. For example, the entry in row 1 and column 2 (0.1) represents the probability that a car in City B today will be in City A tomorrow.

(b) To find the steady state of M, we want to solve the equation (M-1)x = 0, where x is the vector representing the steady-state probabilities of the cars being in City A and City B.

Rewriting the equation as Mx = x, we get:

[ 0.8  0.1 ] [ x1 ]   [ x1 ]

[ 0.2  0.9 ] [ x2 ] = [ x2 ]

This can be rewritten as two equations:

0.8x1 + 0.2x2 = x1 and 0.1x1 + 0.9x2 = x2

Simplifying, we get:

0.2x1 - 0.2x2 = 0 and 0.1x1 - 0.1x2 = 0

This gives us x1 = x2, which means that the steady-state probabilities of the cars being in City A and City B are equal. Let's say this common probability is p. Then we have:

0.8p + 0.2p = p and 0.1p + 0.9p = p

Solving for p, we get:

p = 0.667

Therefore, the steady-state probabilities of the cars being in City A and City B are both 0.667. This means that, in the long run, two-thirds of the cars will be in City A and one-third will be in City B. In other words, the car rental company can expect to have roughly twice as many cars in City A as in City B over time.

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Answer:

60°

Step-by-step explanation:

check the above attachment to verify the answer.

Step-by-step explanation:

x = capacity of Marshfield

y = capacity of Browden

x + y = 210,355

x = y + 4,465

so, using the second equation in the first

(y + 4,465) + y = 210,355

2y + 4,465 = 210,355

2y = 205,890

y = 102,945 (Browden)

x = y + 4,465 = 102,945 + 4,465 = 107,410 (Marshfield)