to calculate the average of the numeric values in a list, the first step is to get the total of values in the list.

Answer:

The surface area is 900cm^2

Step-by-step explanation:

Multiply 3 and 10 to get 30

Then square 30 by multiplying 30 x 30, to get 900.

Answer:

The Surface of the area is 30.

Step-by-step explanation:

Multiply 3 and 10. And you get 30. Hoped this helped : )

Answer:

Perimeter of rectangle = 2(l+b)

= 2(8+5)cm

= 2*13 cm

= 26cm

Step-by-step explanation:

-5x+5y=15(multiply by 2)

3×-2y=-8(multiply by 5)

-10×+10y=30

15×-10y=-40

5x=-10

x=-2

Here,

-5x+5y=15.......(I)

and

3x-2y=8.....(II)

Now,

adding 3 in eqn (II)

so, 6x-5y=8

Now,

combining eqn (I) &(II)

-5x+5y=15

+6x-5y=8

[both 5y is cancelled ]

or, x=7

Now,

in eqn(i)

-5x+5y=15

or, -5*7+5y=15

or, -35+5y=15

or, -35-15=-5y

or, -50=-5y

or, -50/-5=y

[minus is cancelled ]

Therefore, y=10 and x=7

Answer:

I think it is C) 480

Step-by-step explanation:

320÷2=160

160×3=480

Can I please have Brainliest?

There are 480 calories are in the 3-ounce size of the bar.

Multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Green Frog convenience store supplies two types of protein bars.

And, One protein bar has 320 calories in the 2-ounce size.

Now,

For 1 ounce size, calories in One protein bar = 320 / 2

                                                                  = 160

Hence, We get;

For 3 ounce size, calories in One protein bar = 160 x 3

                                                                      = 480

Thus, There are 480 calories are in the 3-ounce size of the bar.

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To solve the equation 2sec^2(x) = 3 - tan(x) in the interval [0, 2π), we can follow these steps:

Rewrite the equation in terms of sine and cosine using the trigonometric identities:

2(1/cos^2(x)) = 3 - sin(x)/cos(x)

Multiply both sides by cos^2(x) to eliminate the denominators:

2 = (3cos^2(x) - sin(x))/cos(x)

Simplify the equation:

2cos(x) = 3cos^2(x) - sin(x)

Rearrange the equation and combine like terms:

3cos^2(x) - 2cos(x) - sin(x) = 0

Unfortunately, this equation cannot be easily solved algebraically to find exact solutions in the given interval [0, 2π). Therefore, the exact solutions for this equation cannot be determined.

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Answer:

40%

8%

15%

37%

Step-by-step explanation:

The solutions are in the image

Answer:

891,962,172,409

Step-by-step explanation:

that is standard form

There are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

To determine the number of possible outcomes when rolling a number cube and picking a cube from 4 colored cubes,

we need to multiply the number of outcomes for each event.

For rolling a number cube (assuming it has 6 sides), there are 6 possible outcomes (1, 2, 3, 4, 5, and 6).

For picking a cube from 4 colored cubes, there are 4 possible outcomes (one for each color).

Now, to calculate the total number of outcomes, multiply the outcomes of each event:

6 (number cube outcomes) x 4 (colored cube outcomes) = 24 possible outcomes.

So, there are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

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There are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

When rolling a number cube, there are six possible outcomes (numbers 1-6). When picking a cube from four colored cubes, there are four possible outcomes. Therefore, the total number of possible outcomes is the product of the number of outcomes from each event: 6 x 4 = 24 possible outcomes.

When rolling a number cube, there are 6 possible outcomes (1, 2, 3, 4, 5, or 6), since a standard number cube has 6 faces, each with a different number.

When picking a cube from 4 colored cubes, there are 4 possible outcomes, one for each color.

To find the total number of outcomes when performing both actions, you can multiply the number of outcomes for each individual action:

Total outcomes = outcomes from rolling a number cube × outcomes from picking a colored cube
Total outcomes = 6 × 4
Total outcomes = 24

So, there are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

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The given matrix is nilpotent of index 3. If matrix A is nilpotent, then its transpose AT is also nilpotent. Nilpotent matrices are not invertible, and as a consequence, the identity matrix minus a nilpotent matrix is always invertible.

(a) To determine the index of the given matrix A, we need to find the smallest positive integer k such that \(A^{k}\) = 0. Computing the powers of A, we have \(A^{2}\) = \(\left[\begin{array}{ccc}0&1&2\\1&0&0\\2&1&0\end{array}\right] t\), \(A^{3}\) = 0, where 0 represents the zero matrix. Therefore, the index of matrix A is 3.

(b) If A is nilpotent, it means that there exists a positive integer k such that \(A^{k}\)= 0. Taking the transpose of both sides, we have (\(A^{k}\))T = 0. Since the transpose of a matrix raised to a power is the same as the transpose of the matrix raised to that power, we have\((A^T)^k\) = 0. Hence, AT is also nilpotent.

(c) Nilpotent matrices are not invertible. To see why, consider a nilpotent matrix A of index k. If A was invertible, there would exist a matrix B such that AB = BA = I, where I is the identity matrix. However, multiplying \(A^{k}\)with B yields (\(A^{k}\)B = 0, contradicting the fact that AB = I. Therefore, nilpotent matrices are not invertible.

(d) If A is nilpotent, then the identity matrix minus A, denoted as I - A, is invertible. To prove this, suppose there exists a matrix B such that (I - A)B = I. Expanding the left side, we get IB - AB = I. Simplifying, we have B - AB = I. Rearranging the terms, we get B = I + AB. Now, multiplying both sides by A, we have AB = A + \(A^2\)B. Since \(A^2\)B is nilpotent,\(A^2\)B = 0. Therefore, B = I + 0 = I. This shows that there exists a unique matrix B such that (I - A)B = I, confirming that I - A is invertible.

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The value of the expression 4.35 * 10^5 - 3 * 10^3 is 4.32 * 10^5

The expression is given as:

4.35 * 10^5 - 3 * 10^3

Rewrite the expression as:

4.35 * 10^5 - 3 * 10^3 = 4.35 * 10^2 * 10^3 - 3 * 10^3

Factor out 10^3

4.35 * 10^5 - 3 * 10^3 = (4.35 * 10^2 - 3) * 10^3

Evaluate the product

4.35 * 10^5 - 3 * 10^3 = (435 - 3) * 10^3

Evaluate the difference

4.35 * 10^5 - 3 * 10^3 = 432 * 10^3

Rewrite as:

4.35 * 10^5 - 3 * 10^3 = 4.32 * 10^5

Hence, the value of the expression 4.35 * 10^5 - 3 * 10^3 is 4.32 * 10^5

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Answer:

40 degrees

Step-by-step explanation:

70-30=40

Answer:

18 months=1.5 years

Step-by-step explanation:

I hope this helps

Answer:

1.5 years

Step-by-step explanation:

1 year = 12 months

18/12 = 1\(\frac{6}{12}\) = 1.5 years

Answer: P=14x-8

Step-by-step explanation:

I will solve this by factoring the numbers

(3x+1)(4x-5)=0

so L and w would be 3x+1,4x-5 order does not matter

Plug in to the perimeter formula and solve

P = 2(L+W)

P = 2(4x-5+3x+1)

P = 2(7x-4)

P = 14x - 8

The magnitude of the number of the minutes in the school is 2.

Although the order of magnitude of zero is not specified, it is occasionally stated to have a magnitude of. Zero is less than any other positive number, and so is its order of magnitude, according to this infinitely negative order of magnitude.

There can be no negative magnitude. The component of the vector that lacks direction is its length (positive or negative).

The order of magnitude is the approximate representation of the logarithmic of the order's value and is typically considered to be 10 taken as the base.

On a scale of 10 logarithmic, the difference in the order of magnitude can be quantified.

The value storage is where you may find the number into the various magnetic.

As a result, the number of minutes spent in school is 2.

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Complete question -

What is the Order of Magnitude of the number of minutes in a school day?

Answer:

a. y=7x or n=7t

b. 42

c. 19 years

d. The answer to that would be that the equation represent an average American uses 7 trees every single year.

Answer:

$563073

Step-by-step explanation:

1. year = $345678 * 1.05

2. year = 1. year * 1.05

...

10. year = 9. year * 1.05

10. year = $536260 * 1.05

10. year = $563073

Given that the resistance remains constant, if the voltage decreases to one-third of its original amount, the resulting current in the circuit is 0.4A

Ohm’s law states that the potential difference between two points is directly proportional to the current flowing through the resistance.

It is expressed as;

V = IR

Where V is the voltage or potential difference, potential difference, I is the current and R is the resistance.

Given that;

Initially, A circuit has a current I = 1.2A

V = IR

R = V/I

R = V/1.2A ...... let this be equation 1

Next, voltage decreases to one-third of its original amount while the resistance remains constant.

Meaning Voltage = 1/3 of V = V/3

Hence;

V = IR

V/3 = IR

From equation 1 ( R = V/1.2A )

V/3 = I × V/1.2A

V/3 = IV/1.2A

We cross multiply

V1.2A = 3IV

I = V1.2A / 3V

I = 1.2A / 3

I = 0.4A

Therefore, given that the resistance remains constant, if the voltage decreases to one-third of its original amount, the resulting current in the circuit is 0.4A

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Answer:

0.4 A

Step-by-step explanation:

When resistance is constant, current is proportional to voltage. When 1/3 the voltage is applied, 1/3 the current will result. (1/3)* (1.2 A) = 0.4 A The resulting current will be 0.4 A.

Answer:

According to the graph, if only one unit was produced, the cost per unit would be $1.00. In reality, the company would not call in its worker and start up the equipment to produce one unit. What safeguard do you think that many manufacturers use to avoid this type of problem?

The per-unit cost will be as follows,

a) Wichita factory has cost function as more up to 25000 units and less for above 25000 units.

b) Piece wise function for cost per units for production of units can be written as

C(x) = cost per unit, will be as follows,

C(x)=1÷x,0 \(\leq\) x \(\leq\) 25000,

=0.8÷x, 25000 \(\leq\) x \(\leq\) 35000,

C) cost per unit for 35000 unit

=C(35000)= 0.8÷35000

= 2.28(10⁻⁵)

Cost per unit  is referred to the cost of goods sold or the cost of sales, is how much money a company spends on producing one unit of the product they sell.

Thus, the cost per unit will be 2.28(10⁻⁵).

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A box with a square base and a top is to be constructed from 10 square meters of material. 40 square meters will maximize the volume that the box can hold.

LSD use among secondary school understudies is a specific concern. More Volume is a proportion of consumed three-layered space. It is frequently evaluated mathematically utilizing SI inferred units or by different supreme units. Volume is characterized as the space involved inside the limits of an article in three-layered space. It is otherwise called the limit of article. Volume is a proportion of consumed three-layered space. It is frequently measured mathematically utilizing the SI determined unit, the cubic meter. The volume of a compartment is by and large comprehended to be the limit of the compartment, how much liquid (gas or fluid) that the holder could hold, instead of how much space the actual holder dislodges. Three layered numerical shapes are additionally relegated volumes.

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its the red one

i learnt it in school

Expression consist of numbers, variables, and mathematical operations. The equation that is true is x²+mx+m= (x+2)².

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

As it is given that the x²+mx+m is a perfect square trinomial, and we know that the general equation of perfect square trinomial  is given as,

ax²+bx+c=0

where a,b and c are real numbers, and a≠0,

if we compare the equation with our equation

\(ax^2+bx+c=0\\x^2+mx+m=0\)

We will get the value of 'a' as 1, b=c=m, therefore, we need a binomial which is when expanded then in its perfect square trinomial the value of b=c, therefore, the only feasible option here is (x+2)².

Hence, the equation that is true is x²+mx+m= (x+2)².

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By evaluating the integrals and using the appropriate limits of integration, we can find the x and y coordinates of the centroid point.

To find the centroid for the area defined by the equations y=2x+4 and y=(2x−3)2+1, we need to calculate the coordinates of the centroid point. The centroid represents the center of mass of the area.

To find the centroid, we first need to determine the limits of integration by finding the points of intersection between the two curves. Setting the two equations equal to each other, we have:

2x + 4 = (2x - 3)^2 + 1

Simplifying the equation, we get:

(2x - 3)^2 - 2x - 3 = 0

Solving this quadratic equation, we find the two points of intersection, which are the limits of integration.

Once we have the limits of integration, we can proceed to calculate the centroid using the formulas:

x = (1/A) ∫[a,b] x f(x) dx

y = (1/A) ∫[a,b] (f(x))^2 dx

where A represents the area of the region, and x and f(x) are the coordinates of the points on the curves.

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Answer to part (b)

y = 12000x

Step-by-step explanation:

This function represented in the graph is a linear equation. Since the function passes through the origin (0,0) we can assume that y = mx for some number m.

According to the graph, the function passes through the coordinate (2,24000)

the 2 in the cooridnate represents the x value, and the 24000 represents the y value. Since the function passes through the origin we can find the number m by dividing the y value of the given cooridinate by the x value of the same cooridinate

m = 24000/2

which can be simplified to

m = 12000

Therfore the line on the graph is a representation of y = 12000x

This equation can be used to solve part (c) by plugging in 10 as the x value, this will return, 120,000

NOTE:

The method which was used to find the function only works if the graph passes through the origin.

The variance of the given returns, which include Year 1 = 14%, Year 2 = 2%, Year 3 = -27%, and Year 4 = -2%, is approximately 0.0341.

To calculate the variance, we first need to find the mean return and then calculate the squared differences from the mean for each return.

The mean return is calculated as (14% + 2% - 27% - 2%) / 4 = -3.25%.

Next, we calculate the squared differences from the mean for each return:

(14% - (-3.25%))^2 = 217.5625

(2% - (-3.25%))^2 = 31.5625

(-27% - (-3.25%))^2 = 529.5625

(-2% - (-3.25%))^2 = 1.5625

The variance is the average of these squared differences:

(217.5625 + 31.5625 + 529.5625 + 1.5625) / 4 = 195.5625 / 4 = 48.890625.

Therefore, the correct answer is option c) .0341 (rounded to four decimal places), which represents the variance of the given returns.

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Answer:

x1= 79, x2= -83

Step-by-step explanation:

seperate into 2 possible cases

x+2=81

x+2= -81

subtract 2 from both sides

x= 79

x= -83

True. The order in which the vectors A and B are drawn does not affect the resultant vector when they are added graphically.

When adding vectors graphically, you represent each vector as an arrow with its magnitude and direction. To find the resultant vector, you place the tail of vector B at the head of vector A (or vice versa), forming a triangle. The resultant vector is then drawn from the tail of the first vector to the head of the second vector. The order in which you draw the vectors does not alter the resulting triangle or its sides.      

Mathematically, vector addition is commutative, which means that the order of addition does not change the result. In this case, adding vector A first and then vector B is equivalent to adding vector B first and then vector A. The resultant vector will have the same magnitude and direction regardless of the order in which the vectors are added.

Therefore, whether you draw vector A first or vector B first, you will obtain the same vector sum (resultant) when adding them graphic ally.

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To properly hedge the balance sheet, Village Bank needs to sell about 2,878 futures contracts, rounded to the closest whole number.

To calculate the number of futures contracts Village Bank must sell to fully hedge the balance sheet, we need to consider the duration gap between assets and liabilities.

The duration gap is calculated as follows:

Duration Gap = (Asset Duration * Asset Value) - (Liability Duration * Liability Value)

Given:

Asset Duration = 12 years

Asset Value = $280 million

Liability Duration = 4 years

Liability Value = $238 million

Duration Gap = (12 * $280 million) - (4 * $238 million)

           = $3,360 million - $952 million

           = $2,408 million

Now, we need to determine the number of futures contracts required to hedge this duration gap. Each T-bond futures contract has an underlying duration of 8 years.

\(\begin{equation}\text{Number of Contracts} = \frac{\text{Duration Gap}}{\text{Duration of Futures Contract}}\end{equation}\)

\(\begin{equation}\text{Number of Contracts} = \frac{\textdollar2,408 \text{ million}}{8 \text{ years}}\end{equation}\)

                  = $301 million

However, we need to convert the contract size from dollars to the quoted price of the futures contract. The quoted price of 104-22 (30nds) corresponds to 104.6875.

\(\begin{equation}\text{Number of Contracts} = \frac{\textdollar301 \text{ million}}{\textdollar104.6875}\end{equation}\)

                  ≈ 2,878 contracts

Rounding to the nearest whole number, Village Bank must sell approximately 2,878 futures contracts to fully hedge the balance sheet.

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Here the length of VT is equal to (x-1) which is equal to 6 and SC is equal to (2x-17) which is equal to 3.

So x=7, VT=6 and SC=3.

Explain length

Length is a fundamental physical quantity used to measure the size of an object or the distance between two points. It is expressed in units such as meters, centimetres, or feet and is used in various fields such as mathematics and physics. The length of a straight line is calculated by finding the distance between its endpoints, while the length of two-dimensional shapes such as rectangles is measured by their perimeter.

According to the given information

We can use the following steps to find x:

Find the length of ST using Pythagoras' theorem as follows:

SV = RV + RS = RV + RT = 6 + (2x - 17) = 2x - 11

UT = UV + VT = 12 + (x - 1) = x + 11

ST² = SV² + UT²

(2x - 11)² + (x + 11)² = ST²

Find the length of VT using Pythagoras' theorem as follows:

TV² = UT² - UV²

TV² = (x + 11)² - 12²

Substitute TV² into the equation in step 1 and solve for x.

After solving for x, we get x=7.

Therefore, VT is equal to (x-1) which is equal to 6 and SC is equal to (2x-17) which is equal to 3.

So x=7, VT=6 and SC=3.

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Answer: 2²/₃ cups of raisins.

Step-by-step explanation:

Question wants to know the number of cups needed for 4 batches of oatmeal bars.

Each batch needs 2/3 cups of raisins to make.

If there are 4 batches to be made therefore, one must multiple the 2/3 cups to make one batch by 4 to find out the number needed to make 4 batches.

= 2/3 * 4

= 8/3

= 2²/₃ cups of raisins.