the cost of a shirt is $72 find the cost of 12 shirts.
\(72\)
​

a) The nth derivative for f(x) = xⁿ is n!.

b) The nth derivative for expression f(x) is (-1)^(n+1) * n! / x^(n+1).

(a) f(x) = xⁿ:

To find the nth derivative of f(x) = xⁿ, we can start by calculating the first few derivatives and looking for a pattern:

f(x) = xⁿ

f'(x) = n x^(n-1)

f''(x) = n(n-1)x^(n-2)

f'''(x) = n(n-1)(n-2)x^(n-3)

...

From this pattern, we can observe that the nth derivative of f(x) is given by:

f ⁿ(x) = n(n-1)(n-2)...(n-(n-1)) x^(n-n)

f ⁿ(x) = n!

Therefore, the nth derivative of f(x) = xⁿ is n!.

(b) f(x) = 1/x:

To find the nth derivative of f(x) = 1/x, we can again start by calculating the first few derivatives and observing the pattern:

f(x) = 1/x

f'(x) = -1/x^2

f''(x) = 2/x^3

f'''(x) = -6/x^4

f''''(x) = 24/x^5

...

From this pattern, we can observe that the nth derivative of f(x) alternates between positive and negative values, and is given by:

f ⁿ(x) = (-1)^(n+1) * n! / x^(n+1)

Therefore, the nth derivative of f(x) = 1/x is (-1)^(n+1) * n! / x^(n+1).

In summary, to find the nth derivative of a function, we can start by calculating the first few derivatives and looking for a pattern. Once we have identified the pattern, we can use it to derive a formula for the nth derivative of the function.

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To determine if the set of vectors (1,2,1,4), (0,1,1,1), and (2,0,1,7) are linearly independent, we need to see if any one of the vectors can be written as a linear combination of the others.

Let's start by assuming that there exist scalars a, b, and c such that:

a(1,2,1,4) + b(0,1,1,1) + c(2,0,1,7) = (0,0,0,0)

We can write this as a system of linear equations:

a + 2c = 0
2a + b = 0
a + b + c = 0
4a + b + 7c = 0

We can solve this system of equations using row reduction:

[ 1  0  2 | 0 ]
[ 2  1  0 | 0 ]
[ 1  1  1 | 0 ]
[ 4  1  7 | 0 ]

R2 = R2 - 2R1:
[ 1  0  2  | 0 ]
[ 0  1 -4  | 0 ]
[ 1  1  1  | 0 ]
[ 4  1  7  | 0 ]

R3 = R3 - R1:
[ 1  0  2  | 0 ]
[ 0  1 -4  | 0 ]
[ 0  1 -1  | 0 ]
[ 4  1  7  | 0 ]

R4 = R4 - 4R1:
[ 1  0  2  | 0 ]
[ 0  1 -4  | 0 ]
[ 0  1 -1  | 0 ]
[ 0  1 -1  | 0 ]

R4 = R4 - R3:
[ 1  0  2  | 0 ]
[ 0  1 -4  | 0 ]
[ 0  1 -1  | 0 ]
[ 0  0  0  | 0 ]

The last row tells us that 0 = 0, which is always true. This means that there are infinitely many solutions to the system of equations, and so the set of vectors is linearly dependent.

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Answer:

(-2, 10), (-1, 7), (0,4), (1, 1), (2, -2)

Draw a line through these points.

Step-by-step explanation:

Start at (0,4) and then going to the right, subtract 3 units on the y axis for each 1x value you go right on. Going to the left, you add 3 units for every 1x unit you go right.

So, you go over right 1, down 3.

Answer:

perimeter = 14

area = 6

Step-by-step explanation:

p = 4 + 3 + 7

a = L × w

2

Perimeter: 14m²n²cm

Area: 28m²n²

height: 4m²

length: 7mn²

base: 3mn²

Perimeter =?

Area=?

Perimeter: a + b + c

Area: length × height

Perimeter: a+b+c

= 4m²+7mn²+3mn²

= 14m²n² cm

Area: l×h

= 4m²×7mn²

= 28m²n²

please mark as brainliest answer pls

Answer:

48

Step-by-step explanation:

check the attached file

Answer:

3 , 11, 25, 45

Diff 8 14 20

Diff 6 6

The second differences are the same. The sequence is quadratic and will contain an n^2 term. The coefficient of n^2 is always half of the second difference. In this example, the second difference is 6. Half of 6 is 3 so the coefficient of n^2 is 3

therefore 3n^2

3 11 25 45

3n^2 3 12 27 48

Remainder 0 -1 -2 -3

Difference -1 -1 -1

linear sequence with nth term -n+1

so nth term of quadratic sequence in 3n^2-n+1

Step-by-step explanation:

LOWASBONMYDADDY!!!!!

The term of the given quadratic sequence is found to be \(a_n=3n^2 - n + 1\) using the principle of mathematical induction.

Given,

In the question:

The quadratic sequence is :

\(3, 11, 25, 45, ...\)

To find the nth term of the quadratic sequence.

Now, According to the question;

The first term of the sequence is 3, the second term is 11, the third term is 25, and the fourth term is 45.

The difference between the first and second terms can be calculated as follows:

\(11-3 = 8\)

The difference between the second and third terms can be calculated as follows:

\(25-11 = 14\)

The difference between the third and fourth terms can be calculated as follows:

\(45-25 = 20\)

The sequence is expressed as follows:

\(3,3+8,11+11,25+20,...\)

The difference between consecutive terms expands by 6.

Use the principle of mathematical induction.

\(6\huge \text(\dfrac{n(n+1)}{2}\huge \text)\)

\(= 3n(n+1)\)

The sequence's nth term can be calculated as follows:

term = \(3n(n+1) - 4n + 1\)

            \(a_n= 3n^2 - n + 1\)

Hence, the term of the given quadratic sequence is found to be \(a_n= 3n^2 - n + 1\) using the principle of mathematical induction.

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Answer:

(-4, 2).

Step-by-step explanation:

8x + 5y=-22

-3x - 5y = 2   Adding the 2 equations:

5x = -20

x = -4.

Substitute x = -4 in the first equation:

8(-4) + 5y = -22

5y = -22 + 32

5y = 10

y = 2.

Answer:

\(x=-4,\:\\y=2\)

Step-by-step explanation:

\(\begin{bmatrix}8x+5y=-22\\ -3x-5y=2\end{bmatrix}\\\mathrm{Multiply\:}8x+5y=-22\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:24x+15y=-66\\\mathrm{Multiply\:}-3x-5y=2\mathrm{\:by\:}8\:\mathrm{:}\:\quad \:-24x-40y=16\\\\\begin{bmatrix}24x+15y=-66\\ -24x-40y=16\end{bmatrix}\\\\-24x-40y=16\\+\\\underline{24x+15y=-66}\\-25y=-50\\\begin{bmatrix}24x+15y=-66\\ -25y=-50\end{bmatrix}\\-25y=-50\\\mathrm{Divide\:both\:sides\:by\:}-25\\\frac{-25y}{-25}=\frac{-50}{-25}\\y=2\\\)

\(\mathrm{For\:}24x+15y=-66\mathrm{\:plug\:in\:}y=2\\24x+15\times\:2=-66\\24x+30=-66\\24x+30-30=-66-30\\24x=-96\\\frac{24x}{24}=\frac{-96}{24}\\x=-4\\\\\\x=-4,\:y=2\)

Answer:

x=4

Step-by-step explanation:

13.9-2x=5.9

We simplify the equation to the form, which is simple to understand

13.9-2x=5.9

We move all terms containing x to the left and all other terms to the right.

-2x=+5.9-13.9

We simplify left and right side of the equation.

-2x=-8

We divide both sides of the equation by -2 to get x.

x=4

Answer:

x = 4

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Step-by-step explanation:

Correct option is A)

Answer:

The equation of the exponential function will be:

\(f\:\left(x\right)\:=\:ab^x\)

          \(=\:\frac{3}{2}\left(2\right)^x\)

Step-by-step explanation:

Given the table

Day         Bacteria

1               3

2              6

3              12

4              24

5              48

as

and

so it is indeed an exponential function

As we know that the exponential function is of the form

\(f\:\left(x\right)\:=\:ab^x\)

As we know that the y-intercept of \(f\:\left(x\right)\:=\:ab^x\) is (0, a).

so

\(\frac{3}{a}=2\)        ∵ common ratio = successor y-value ÷ previos y-value

\(a=\frac{3}{2}\)

so the value of a will be: 3/2

We also know that the common factor i.e. multiplier is 2 in this table, we know the value for b is 2.

Therefore, the equation of the exponential function will be:

\(f\:\left(x\right)\:=\:ab^x\)

          \(=\:\frac{3}{2}\left(2\right)^x\)

Answer:

The answer to Y/X is 4/1

The rate of change of depth of water at a water depth of 6 ft is -11.22 ft/hr (decreasing).

The given rate at which water is leaking from the tank is 2 ft³/hr.The height of the cone, h = 14 ftThe base radius, r = 5 ftLet us consider the similar triangles formed between the cone and its frustum (due to the change in the water depth). Let H be the height of the water at any time, and h the height of the cone. The volume of the cone at any time, V, is given by;V = 1/3 πr²hAnd the volume of the water at any time, V', is given by;V' = 1/3 πr²HSince the water level is reducing at a constant rate, dH/dt = -2 ft/hr.

The relationship between the height of the cone and its radius can be obtained by using the similar triangles formed by the cone and its frustum. The relation is given as;h/r = H/(R - r)Where R is the radius of the frustum.The radius of the frustum is given by;R = r + (H/h) (R-r)Substituting the value of R into the expression for the volume of the frustum gives;V' = 1/3 πr²H + πH²/3h(H/h + 1) (R - r)².

Now, differentiate both sides of the equation with respect to time; dV'/dt = d/dt [1/3 πr²H + πH²/3h(H/h + 1) (R - r)²]Let us substitute r = 5 ft, h = 14 ft, and H = 6 ft into the above equations in order to find dR/dt; dV'/dt = d/dt [1/3 π(5)²(6) + π(6)²/3(14/6 + 1) (R - 5)²]dV'/dt = π/3 [25(2) + 36/(4/3) (dR/dt)²]Hence;2 = -2π/3 [25(2) + 36/(4/3) (dR/dt)²]dR/dt = -[25(2)(3/2π) + 3/4(dV'/dt)²]½dR/dt = -11.22 ft/hr .Therefore, the rate of change of depth of water at a water depth of 6 ft is -11.22 ft/hr (decreasing).

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Step 1: Write out the expression to simplify

Step 2: Remove the bracket using distribution property

Step 3: Rewrite the resulting expression in order of degree and state the degree and the number of terms

The degree is 3 (third degree) as the highest power of the variable is 3, there are three terms in the expression

Hence, the expression is a cubic expression (degree 3) and a trinomial (3 terms)

EXPLANATION

We can affirm that the length of the adjacent leg is 5 units and the length of the hypotenuse is 8 units.

As given, the length of the third side is 6.245 units.

Now, computing sin A give us the following expression:

The solution is 1249/1600

Answer: D: Y=(x-1)(x-1)

Step-by-step explanation:

The function described by the graph is \((x-1)^2\).

Therefore, the correct answer is Option D. y = ( x - 1 ) ( x - 1 )

Given data:

The function is represented as f(x) = y

Now, the value of f(x) is plotted below:

To plot the graph, start by determining some key points and then connecting them.

When x = 0:

f(0) = 1

So, the point is (0, 1).

When x = 1:

f(1) = 0

So, the point is (1, 0).

When x = 2:

f(2) = 1

So, the point is (2, 1).

The graph of \(f(x) = (x - 1)^2\)  is a parabola that opens upwards. The vertex of the parabola is at the point (1, 0), which corresponds to the minimum value of the function.

As x moves further away from 1 in either direction, the function increases.

Hence, the parabolic function is \(f(x) = (x - 1)^2\).

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Using the Central Limit Theorem, the given statements are true or false in following

a) True

b) True

c) True

d)True

e) True

a) From the definition of central limit theorem, by law of large number to sample average converge almost slowly to the population average.

So, based on CLT the sample mean be used a3 gond estimator of the population mean assuing that the sample size. sufficiently large i.e ., True.

b) Same reason as (a) , based on CLT the usually considers that sample 51Z6 30 is sufficiently large is true

c) If we generate 1000 samples of Binomial (10;0.3)distribution are plot a histogram then it looks like normal distribution.

So, the Central Limit Theorem be applied to both discrete and continols Fandom variables is true.

d) Whatever be the parent distribution , if sample size ,n is large then sample mean means

converges in probability to the population mean.

So, the given option (d) is true .

e) If population size is normally distributed then sample mean is also normally distributed for all sample size.

So, option(e) is also true.

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Complete question:

Problem Central Limit Theorem) _ Are the following statements true or false?

a)Easy. Based the Central Limit Theorem_ the sample mean be used a3 gond estimator of the population mean assuing that the sample size. sufficiently large.

b)Easy. Then applying the Central Limit Theorem. l usually conziders that sample 51Z6 30 is sufficiently large.

c)Easy. the Central Limit Theorem be applied to both discrete and continols Fandom variables .

d): Assuming that the sample size is sufficiently large the Central Limit Theorem permits draw conclusions about the population based strictly sample data. and without having aIV knowledge about the distribution of the underlying population:

(e) Moderate_ Assuming that the population is normally distributed_ the sampling distribution of the sample mean is normally distributed for samples of all sizes_

Answer:

4. (2,1) 5. (-2,1) 6. (8, 80)

Step-by-step explanation:

2x + 4y - 2x + 2y = 8 - 2

6y = 6

y = 1

2x + 4 = 8

2x = 4

x = 2

(2,1)

3x + 4y + 6x - 4y = -2 - 14

8x = -16

x = -2

-6 + 4y = -2

4y = 4

y = 1

(-2,1)

multiply first equation by 4

4y = 40x

4y + 40x + 6y = 40x + 800

10y = 800

y = 80

80 = 10x

x = 8

(8, 80)

Answer:

4³

Step-by-step explanation:

  16 x 4

(4 x 4) x 4 = 64

The three vectors that form an orthonormal basis for R3 are:

u = (0.6, -0.8, 0)
v = (1, 0, 0)
w = (0, 0, 0.6)

To find the missing coordinates such that the three vectors form an orthonormal basis for R3, we need to use the concept of coordinates, vectors, and orthonormality.

First, let's define the three vectors as u = (0.6, -0.8, 0), v = (1, 0, 0), and w = (0, 0, 0.6).

To form an orthonormal basis for R3, the three vectors need to be orthogonal to each other and have a magnitude of 1.

Orthogonality means that the dot product of any two vectors is 0. So we need to find the missing coordinates of w such that:

u • v = 0
u • w = 0
v • w = 0

Since u and v are already orthogonal to each other, we only need to find the missing coordinates of w such that it is orthogonal to both u and v.

Let's start with u • w = 0:

0.6 * 0 + (-0.8) * 0 + 0 * 0.6 = 0

This equation is already satisfied, so we don't need to find any missing coordinates for w in relation to u.

Now let's look at v • w = 0:

1 * 0 + 0 * 0 + 0 * 0.6 = 0

Again, this equation is already satisfied, so we don't need to find any missing coordinates for w in relation to v.

Since both equations are satisfied, the missing coordinates of w are (0, 0).

Therefore, the three vectors that form an orthonormal basis for R3 are:

u = (0.6, -0.8, 0)
v = (1, 0, 0)
w = (0, 0, 0.6)

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Answer:

16

Step-by-step explanation:hope this helps

a/8=2

Step 1: Multiply both sides by 8.

a/8=2

(a/8)*(8)=(2)*(8)

a=16

Answer:

4%

Step-by-step explanation:

The formula for simple interest is I = Prt, where I is the interest, P is the principal amount, r is the interest rate, and t is the time in years.

In this case, we know that:

P = £500 (the principal amount)

I = £40 (the interest earned)

t = 2 years (the time the money was invested)

We can rearrange the formula to solve for r:

r = I / Pt

Substituting the given values, we get:

r = 40 / (500 x 2)

r = 0.04 or 4%

Therefore, the simple interest rate per annum is 4%.

The area covered by the pool and the cement walkway is 304  square feet. The width of the walkway would be 5 feet

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Let x be represent the width of the walkway.

The pool measures 25 ft by 10ft . If the walkway must have a uniform width around the entire pool, then the total length of the pool and the walkway =  25+ x + x = 25 + 2x

The total width of the pool and the walkway = 10 + x + x = 10 + 2x

The area covered by the pool and the cement walkway is 304  square feet. This means that;

(25 + 2x)(10 + 2x) = 304

250 + 50x + 20x + 4x^2 = 304

4x^2 + 70x + 250 - 304 = 0

4x^2 + 70x - 54 = 0

x(x + 20) - 5(x + 20) = 0

(x - 5)(x + 20) = 0

x = 5 or x = - 20

Thus The width cannot be negative.

Therefore, the width of the walkway is 5 feet.

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Answer:

Step-by-step explanation:

Este es muy fácil, simplemente dibujas los nueve corrales y pones diez vacas en entre. ¿¿Como??

Por ejemplo, tú tienes algo como esto

D

I

E

Z

V

A

C

A

S

Donde, cada letra es la vacas tú tienes, y pones en el corral. Esta camina, tienes poner diez vacas en entre nueve corrales. Espero que me entiendas. Gracias

The erosion occurs at a rate of 2/1000 m/years. Over 1,000,000 years, the erosion will be 2,000 meters.

Rate is a ratio between one quantity to another quantity. Rate is also a measure of how fast a quantity changes when another quantity changes. For instance, velocity is a rate to measure the change of distance per amount of travelled time.

Suppose we have two quantities: x and y, with rate of change in y per change in x is denoted by dy/dx, then

y = dy/dx · x

In the given problem:

y = length of erosion

t = time

dy/dt = 2 meters / 1000year = 2/1000 meters/year

Then,

y = dy/dt · t

  = 2/1000 · 1,000,000 = 2,000 meters

Hence, over  1,000,000 years, the regional erosion = 2,000 meters

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Answer:

45 = 40 tens + 5

Step-by-step explanation:

Hope this helps

Brainliest pls ❤️

Answer:

4

Step-by-step explanation:

4x10=40 40+5=45

Answer:

F

Step-by-step explanation:

The x and y do not match up

Answer:

It is F.

Step-by-step explanation:

It is F because all the x's are the same as that cannot happen.

To calculate the Value-at-Risk (VaR) for this investment at a 99% confidence level, we need to determine the loss amount that will be exceeded with a probability of only 1% (i.e., the worst-case loss that will occur with a 1% chance).

Given that there is a 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million, we can express this as:

Loss Amount | Probability

$10 million | 0.5%

$1 million | 99.5%

To calculate the VaR, we need to find the loss amount that corresponds to the 1% probability threshold. Since the loss of $10 million has a probability of 0.5%, it is less likely to occur than the 1% threshold. Therefore, we can ignore the $10 million loss in this calculation.

The loss of $1 million has a probability of 99.5%, which is higher than the 1% threshold. This means that there is a 1% chance of the loss exceeding $1 million.

Therefore, the Value-at-Risk (VaR) for this investment at a 99% confidence level is $1 million.

The Value-at-Risk (VaR) for this investment at a 99% confidence level is $1,045,000.

To calculate the Value-at-Risk (VaR) for this investment at a 99% confidence level, we need to determine the loss amount that will be exceeded with only a 1% chance.

Given that the investment has a 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million, we can calculate the VaR as follows:

VaR = (Probability of Loss of $10 million * Amount of Loss of $10 million) + (Probability of Loss of $1 million * Amount of Loss of $1 million)

VaR = (0.005 * $10,000,000) + (0.995 * $1,000,000)

VaR = $50,000 + $995,000

VaR = $1,045,000

Therefore, the Value-at-Risk (VaR) for this investment at a 99% confidence level is $1,045,000.

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