a bank pin is a string of four digits, each digit 0-9. how many choices are there for a pin if the last digit must be odd and all the digits must be different from each other? a. 9 ⋅ 8 ⋅ 7 ⋅ 5 b. 5 ⋅ 103 c. 10 ⋅ 9 ⋅ 8 ⋅ 5 d. 10 ⋅ 9 ⋅ 8 ⋅ 7

Based on the arithmetic sequence with the first term −5 and the common difference 4 is 660, we could find m = 20.

To find the sum of the first m terms of an arithmetic sequence, we can use the formula:

sum = (m/2)(2a + (m-1)d),

where a is the first term,

d is the common difference,

and m is the number of terms.

In this case, we are given a = −5, d = 4, and sum = 660. We can plug these values into the formula and solve for m:
660 = (m/2)(2(-5) + (m-1)(4))
660 = (m/2)(-10 + 4m - 4)
660 = (m/2)(4m - 14)
1320 = m(4m - 14)
0 = 4m^2 - 14m - 1320

Now we can use the quadratic formula to solve for m:
m = (-b ± √(b^2 - 4ac))/(2a)
m = (-(−14) ± √((−14)^2 - 4(4)(-1320)))/(2(4))
m = (14 ± √(196 + 21120))/8
m = (14 ± √21316)/8
m = (14 ± 146)/8

Now we have two possible values for m:
m = (14 + 146)/8 = 160/8 = 20
m = (14 - 146)/8 = -132/8 = -16.5

Since m must be a positive integer, we can conclude that m = 20. Therefore, the sum of the first 20 terms of the arithmetic sequence is 660.

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Answer:

Letter C

Step-by-step explanation:

A function has to have no repeating x-intercepts.

Answer: B (The cost of a notebook is $0.75, and the cost of a folder is $0.25.)

Step-by-step explanation:

No need for explanation. i know i’m right!!

The power series solution of the differential equation about x0 = 1 has a radius of convergence of 1.

To find the minimum radius of convergence R of power series solutions about the ordinary point x0 = 1 for the given differential equation, we need to use the Cauchy-Hadamard formula. The formula states that the radius of convergence R is given by:

R = 1/lim sup(|an|)^(1/n)

where an is the nth coefficient of the power series solution.

First, we need to find the power series solution of the differential equation about x0 = 1. We can assume that the solution is in the form of a power series:

y(x) = ∑ an (x-1)^n

We can differentiate this power series to find the derivatives needed to substitute into the differential equation. After substituting and simplifying, we get:

∑ (n+2)(n+1)an (x-1)^n + ∑ (n+1)an (x-1)^n + 4∑ an (x-1)^n = 0

Next, we need to find the coefficients an. We can do this by equating the coefficients of each power of (x-1) to zero. The first few coefficients are:

a0 = y(1)

a1 = y'(1)

a2 = y''(1)/2!

Substituting these coefficients into the formula for R, we get:

R = 1/lim sup(|(n+2)(n+1)/2!|^(1/n) + |(n+1)/1!|^(1/n) + |4/0!|^(1/n))

Taking the limit as n approaches infinity, we get:

lim sup(|(n+2)(n+1)/2!|^(1/n) + |(n+1)/1!|^(1/n) + |4/0!|^(1/n)) = 1

Therefore, the minimum radius of convergence R is:

R = 1/1 = 1

So the power series solution of the differential equation about x0 = 1 has a radius of convergence of 1.

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Answer:

Read below

Step-by-step explanation:

Notebooks:

275 x 11 = 3,025

laptops:

Is this a mistake but are the desktop computers and laptop computers the same because laptops and desktops are two different things but they are BOTH computers.

300 x ?

How many laptops did you get?

Answer:

n=3025.........d=6000

Step-by-step explanation:

you multiply the cost of the item (275$ or 300$) by the quantity. Since you have 11 notebook computers and 20 desktop computers, you multiply the cost of each by the quantity (275$ x 11) and (300$ x 20)  to get your answer.

Ex.-

275 x 11 = 3025$  =   n=3025$

300 x 20 = 6000$   = d=6000$

Happy to help! :)

To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.

To find a quadratic equation with the y-intercept and vertex, we can follow these steps:

For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:

3 = a(0)^2 + b(0) + c

1 = a(-2)^2 + b(-2) + c

Simplifying these equations, we get:

c = 3

4a - 2b + c = 1

By substituting c = 3 into the second equation, we can solve for a and b:

4a - 2b + 3 = 1

4a - 2b = -2

2a - b = -1

By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:

y = x^2 + x + 3

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To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.

Example:

Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).

To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.

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1. An exponential function to represent the spread of Ben's social media post is \(f(x) = 2(3)^x\)

2. An exponential function to represent the spread of Carter's social media post is \(f(x) = 10(2)^x\)

3. A graph of each function with three points for each curve is shown below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x) = a(b)^x\)

Where:

Based on the table of values, the initial value is 2. Next, we would determine the common ratio (b) as follows;

Common ratio, b = a₂/a₁

Common ratio, b = 6/2 = 3.

Therefore, the required exponential function is given by;

\(f(x) = 2(3)^x\)

Part 2.

For Carter's social media post, we have the following exponential function:

\(f(x) = a(b)^x\\\\f(x) = 10(2)^x\)

Part 3.

In this scenario and exercise, we would use an online graphing calculator to plot the above exponential functions as shown in the graph attached below.

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The expression is simplified to 1/2(6²/4²)

Index forms are simply defined as those mathematical models that are used in the representation of values or variables that are too large or small in more convenient forms.

These index forms are known with other names which are;

Note that the rules of indices are;

From the information given, we have that;

36/32

Find the perfect squares

6/2× 16

6²/2(4)²

1/2(6²/4²)

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Answer:

Well, it really just comes down to factoring the area into all of its components.

1 X 32 Perimeter is 2 + 64, or 66 m

2 X 16 Perimeter is 4 + 32 or 36 m

4 X 8 Perimeter is 8 + 16 or 24 m

8 X 4

16 X 2

32 X 1

Please note that the last 3 are just the first 3 in a different orientation and I don’t consider them to be unique. I noted them as a self-check to my own work. So we have 3 rectangles giving an area of 32 square meters and perimeters as noted above.

Answer:

dimensions which would give a rectangle a perimeter of 32 inches:

1 x 15

2 x 14

3 x 13

4 x 12

5 x 11

6 x 10

7 x 9

8 x 8

Step-by-step explanation:

Answer:

$7.47

Step-by-step explanation:

Take the number of pounds and multiply by the price per pound

3 * 2.49

7.47 for 3 pounds of apples

Answer:

7.49

Step-by-step explanation:

Given: 3 pounds, and 2.49 for each pound

Multiply:

2.49 × 3

 ₁   ₂    

 2.49

×      3

----------

 7. 47

Mrs. Ella bought 3 pounds of apples for $7.49

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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Answer:

After selling 98 cups, she made $98

Step-by-step explanation:

If she sold 98 cups, and each one went for $1, then you can set up an equation:

98(1)=98

Answer:

Ashley made $98.

Step-by-step explanation:

If 1 cup = $1, then you multiply the cups by 98 meaning you also must multiply $1 by 98 to get a total of $98.

Answer and Step-by-step explanation:

The answer will be the first answer choice, in which both lines would be the same lines as the original shape.

This is because the figure is being dilated by the point P, so it will only increase in length one direction, instead of making the entire triangle get bigger and surround the original triangle.

#teamtrees #PAW (Plant And Water)

The solution for the absolute value equation is x = 10 and x = -14

In this question,

Two thirds times the absolute value of the quantity x plus 2 end quantity minus 8 equals 0. The equation for this statement is 2/3 lx + 2l -8 =0.

The solution for the equation is

\(\frac{2}{3}\) lx + 2l -8 =0

\(\frac{2}{3}\) lx + 2l = 8

Multiply by 3/2 on both sides,

\(\frac{2}{3}\) lx + 2l = 8

\(\frac{2}{3}\) ×\(\frac{3}{2}\)lx + 2l =8×\(\frac{3}{2}\)

=> x +2 = 12

Case 1: Take as positive value

=> x + 2 = 12

=> x = 12 - 2

=> x = 10

Case 2: Take as negative value

=> -(x +2) = 12

=> -x - 2 = 12

=> -x = 12 + 2

=> -x = 14

=> x = -14

Hence, we can conclude that the solution for the absolute value equation is x = 10 and x = -14 is the correct answer

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ANSWER:

500.5 m²

STEP-BY-STEP EXPLANATION:

To know how much artificial grass should be purchased to cover the athletic field, we must calculate the area corresponding to the figure.

The area of a trapezoid has the following formula:

Where b is the small base, B is the large base and h is the height, we substitute and calculate the area, like this:

It is necessary to purchase the amount of 500.5 m² to be able to cover the athletic field

Answer: B

Step-by-step explanation:t+4+3−2.2t

Add 4 and 3 to get 7.

t+7−2.2t

Combine t and −2.2t to get −1.2t.

−1.2t+7

The power in each sideband is 20.25 W and the total power of the signal is 439.05 W.

When an amplitude modulated signal is transmitted, two sidebands are generated, each containing the message signal.

The carrier is transmitted along with the sidebands.

The amount of power in each sideband depends on the modulation index.

The given carrier power (Pc) = 250 W.

The modulation index (m) = 0.9.

The total power (Pt) in the signal can be calculated using the following formula:

Pt = Pc(1 + (m^2/2))Pt = 250(1 + (0.9^2/2))Pt = 439.05 W

The power in each sideband can be calculated using the following formula:

Psb = (m^2/4)PcPsb = (0.9^2/4) × 250Psb = 20.25 W

Thus, the power in each sideband is 20.25 W and the total power of the signal is 439.05 W.

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Answer:

21.98 cm

Step-by-step explanation:

Circumference of a circle is found by using this formula:

\(\large\tt \:\:\:\:\:\:\:\:\:\:\:C=2\pi r\:\:\:\:\) or \(\:\:\:\:\:\large\tt C =\pi d\)

Therefore, the circumference of a circle is 21.98cm

\(\log\left(\frac{10}{y}\right) = \log(10) - \log(y)\)

The general rule is

\(\log\left(\frac{A}{B}\right) = \log(A) - \log(B)\)

Other log rules are

\(\log(AB) = \log(A) + \log(B)\)

\(B\log(A) = \log(A^B)\)

It would take Cookie Monster 6,000,000 hours to make 6 million batches of cookies, assuming he doesn't take any breaks and all of his ovens continue to function perfectly.

If it takes 1 hour to cook a batch of cookies and Cookie Monster has 15 ovens, working 24 hours a day, every day for 5 years, then the total amount of batches of cookies he can make in 5 years is:

Batches of cookies = (15 ovens) × (24 hours) × (365 days) × (5 years)

Batches of cookies = 1,314,000

This is the number of batches of cookies he can make in 5 years working non-stop.

To find out how long it takes him to make 6 million batches, we can set up a proportion.

Let x be the number of hours it takes to make 6 million batches of cookies:

x hours / 6,000,000 batches = 1 hour / 1 batch

Solving for x, we get:

x = 6,000,000 hours

Therefore, it would take Cookie Monster 6,000,000 hours to make 6 million batches of cookies, assuming he doesn't take any breaks and all of his ovens continue to function perfectly.

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Answer:

34+12x=100 12x=66 x=66/12=11/2 answer:11/2

Step-by-step explanation:

Answer:

\(12n+34>100\)

Step-by-step explanation:

Let d be the number of days.

We have been that each day Katie finds 12 more seashells on beach, so after collecting shells for d days Katie will have 12d shells.  

We are also told that Katie already has 34 seashells in her collection, so total number of shells in Katie collection after d days will be: \(12n+34\)

As Katie wants to collect over 100 seashells, so the total number of shells collected in d days will be greater than 100.

Answer:

\(\sqrt{18}\) inches

Step-by-step explanation:

A = 18 sqr inches

s =  \(\sqrt{18}\)

A = s^2

A =  \(\sqrt{18}\) inches x \(\sqrt{18}\) inches

A = 18 sqr inches

The solution to the linear system is unique solution which is  x₁ = 1/6, x₂ = 3/2, and x₃ = 17/6.

The correct answer is option  A.

To solve the given system of linear equations using elementary row operations and back substitution, let's start by representing the augmented coefficient matrix:

[1  -4  5  |  23]

[2   1   1  |  10]

[-3  2  -3 |  -23]

We'll apply row operations to transform this matrix into echelon form:

1. Multiply Row 2 by -2 and add it to Row 1:

[1  -4   5   |  23]

[0   9   -9  |  -6]

[-3  2  -3  |  -23]

2. Multiply Row 3 by 3 and add it to Row 1:

[1  -4  5   |  23]

[0   9  -9  |  -6]

[0   -10 6  |  -68]

3. Multiply Row 2 by 10/9:

[1  -4  5    |  23]

[0   1   -1   |  -2/3]

[0   -10 6  |  -68]

4. Multiply Row 2 by 4 and add it to Row 1:

[1  0   1   |  5/3]

[0  1   -1  |  -2/3]

[0  -10 6  |  -68]

5. Multiply Row 2 by 10 and add it to Row 3:

[1  0   1   |  5/3]

[0  1   -1  |  -2/3]

[0  0   -4  |  -34/3]

Now, we have the augmented coefficient matrix in echelon form. Let's solve the system using back substitution:

From Row 3, we can deduce that -4x₃ = -34/3, which simplifies to x₃ = 34/12 = 17/6.

From Row 2, we can substitute the value of x₃ and find that x₂ - x₃ = -2/3, which becomes x₂ - (17/6) = -2/3. Simplifying, we get x₂ = 17/6 - 2/3 = 9/6 = 3/2.

From Row 1, we can substitute the values of x₂ and x₃ and find that x₁ + x₂ = 5/3, which becomes x₁ + 3/2 = 5/3. Simplifying, we get x₁ = 5/3 - 3/2 = 10/6 - 9/6 = 1/6.

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Answer:

15 2/3

Step-by-step explanation:

1 x 2/3 + 15=2/3+15=15 2/3

Answer: 15 2/3

Step-by-step explanation:

1. Times the 1 and the two-thirds.

1 * 2/3 = 2/3

2. Add two-thirds and fifteen.

2/3 + 15 = 15 2/3

Answer:

Protractor

Step-by-step explanation:

You use a ruler to draw a straight line.

You use a protractor to draw an angle.

A straight line is to a ruler and an angle is to protractor.

"A protractor is a simple measuring instrument that is used to measure angles. A common protractor is in the shape of a semicircle with an inner scale and an outer scale and with markings from 0 degrees and 180 degrees on it."

"A math ruler is used to measure the length in both metric and customary units. The rulers are marked with standard distance in centimeters in the top and inches in the bottom and the intervals in the ruler are called hash marks."

A straight line is to a ruler and an angle is to protractor.

A protractor is a simple measuring instrument that is used to measure angles. A common protractor is in the shape of a semicircle with an inner scale and an outer scale and with markings from 0 degrees and 180 degrees on it.

Cosine is a trigonometric function that for an acute angle is the ratio between the leg adjacent to the angle when it is considered part of a right triangle and the hypotenuse.

A math ruler is used to measure the length in both metric and customary units. The rulers are marked with standard distance in centimeters in the top and inches in the bottom and the intervals in the ruler are called hash marks.

A calculator is a device that performs arithmetic operations on numbers. The simplest calculators can do only addition, subtraction, multiplication, and division.

Hence, A straight line is to a ruler and an angle is to protractor.

Option (C) is correct.

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Answer:

P = 5/12

Step-by-step explanation:

Answer:

Asiatic Registration Bill of 1906.

Step-by-step explanation:

The first passive resistance campaign was started in Johannesburg in 1907 with, and for, the wealthy South African Indian merchants whom he had so long represented.’ Gandhi’s first passive resistance campaign began as a protest against the Asiatic Registration Bill of 1906.

Answer:

given p(x)= 5x^3-7x^2-ax-28

(x-4) is a factor of 5x^3-7x^2-ax-28

=>p(4)=0

=>5(4)^3-7(4)^2-4a-28=0

=>320-112-4a-28=0

=>-4a=-180

=>a=180/4

=>a=45

Step-by-step explanation:

x=a

The dropping degree temperature will be  -12°.

A drop of 17 degrees means subtract 17  from given temperature

∴5°-17°=-12°

so, the Temperature drop will be -12°

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Part A: You have the followinf system of inequalities:

In order to determine the solution of the previous system, solve the previous inequalities for y:

Now, take the previous inequalities as equations and graph the lines with a solid line (it means that values on the line are included in the solution for each inequality, due to the symbol of the inequality is ≤ and ≥):

The solid red line is the line for the first inequality. Due to in this inequality you have the symbol ≤, the valid solutions are all values below the line. The red shaded region has all solutions for this inequality.

The blue solid line represents the second inequality. Again, due to this inequality has the symbol ≥, it means that the valid solutions are all values above the line. The blue shaded region represent allsolutions of the second inequality.

The solution to the system is given by the region at which the red region and blue region overlap between them. As you can notice, the regions start to overlap at point (-6,9).

Part B: The point (5,1) is in the region of the overlapping of the blue and red region. It means that point (5,1) is a solution of the system.

Part C: you can select any point of the solution region. For instance, the point (3,1). This solution means that with the money Michael has, He is able to buy 3 sandwichs and 1 hot lunch.