A study of 860 u.s. atms (automated teller machines) found that the average surcharge for withdrawals from a competing bank was $1.15. (source: public interest research groups) what is known about the atms from a competing bank?

[tex]c^2 = a^2 + b^2 - 2ab \cos C \\ \\ 55^2 = 24^2 + 40^2 - 2(24)(40)\cos C \\ \\ \cos C=\frac{55^2 - 24^2 - 40^2}{-2(24)(40)} \\ \\ C=\cos^{-1} \left(\frac{55^2 - 24^2 - 40^2}{-2(24)(40)} \right) \\ \\ \cos C=-\frac{283}{640} \\ \\ C=\boxed{\arccos \left(\-frac{283}{640} \right)}[/tex]

[tex]C=\boxed{\arccos \left( - \frac{283}{640} \right)}[/tex]

The sum of the given series is 49 and it converges to infinity.

According to the statement

we have given that a series which is 7, -8, 64/7, 512/49

And we have to find that the series is converges or diverges.

So, For this purpose,

The nth term in the series is 6 multiplied by the (n-1)th power of -8/7:

So,

[tex]a_{1} = 7(\frac{-8}{7} )^{1-1}[/tex]

[tex]a_{2} = -8(\frac{-8}{7} )^{2-1}[/tex]

[tex]a_{3} = \frac{64}{7} (\frac{-8}{7} )^{3-1}[/tex]

And so on then

Sum of the series become to the nth partial sum

[tex]S_{N} = 7(1 +\frac{-8}{7} + ......+ (\frac{-8^(n-2)}{7^(n-2)}) + (\frac{-8^(n-1)}{7^(n-1)}))[/tex]

Multiplying both sides by -8/7 gives

[tex]\frac{-8}{7} S_{N} = 7(\frac{-8}{7} +\frac{-8^{2} }{7^{2}} + ......+ (\frac{-8^(n-1)}{7^(n-1)}) + (\frac{-8^n}{7^n}))[/tex]

and subtracting this from [tex]S_{N}[/tex] gives

[tex]\frac{-1}{7} S_{N} = 7(1-\frac{-8^n}{7^n} )[/tex]

[tex]S_{N} = 49 (-1 + (8/7)^n)[/tex]

Now the sum of the series is 49 and the it converges to infinity.

So, The sum of the given series is 49 and it converges to infinity.

Learn more about the Convergence of series here

https://brainly.com/question/23804543

#SPJ1

The Laplace transform of the given function is [tex]f(s)=\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]

Given,

[tex]f(t)=\left \{ {{t, 0\leq t < 5} \atop {0,t\geq 5}} \right.[/tex]

Write the function in unit step function.

[tex]f(t)=t(u_{0}(t)-u_{5} (t))[/tex]

      = [tex]t(1-u_{5}(t))[/tex]                       ∵[tex]u_{0} (t)=1[/tex]

      = [tex]t-tu_{5} (t)[/tex]

[tex]f(t)=t-tu_{5} (t)[/tex]

In order to make it easier to take the Laplace transform of the function, we can follow the steps:

[tex]f(t)=t-tu_{5} (t)[/tex]

      = [tex]t-(t-5+5)u_{5} (t)[/tex]

      = [tex]t-(t-5)u_{5} (t)+5u_{5} (t)[/tex]

[tex]f(t)=t-(t-5)u_{5} (t)+5u_{5} (t)[/tex]

We need to find the Laplace transform of f(t).

Apply Laplace transform on both sides,

£[tex][f(t)=[/tex]£[tex](t)-[/tex]£[tex](t-5)u_{5} (t))+5[/tex]£[tex](u_{5} (t))[/tex]

         = [tex]\frac{1}{s^{2} } -e^{-s}[/tex]£[tex](t)+5(\frac{e^{-5s} }{s} )[/tex]

         = [tex]\frac{1}{s^{2} } -e^{-5s} (\frac{1}{s^{2} } )+\frac{5se^{-5s} }{s^{2} }[/tex]

        = [tex]\frac{1-e^{-5s}+5se^{-5s} }{s^{2} }[/tex]

       = [tex]\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]

[tex]f(s) =\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]

Learn more about Laplace transform here: https://brainly.com/question/17190535

#SPJ4

The first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608

For given question,

We have been given the recursive formula of a sequence.

[tex]a_{k+1}=\frac{1}{3}{a_k}^2[/tex]

Also, the first term of the sequence is,

a1 = 6

Substitute k = 1 in given recursive formula.

⇒ [tex]a_{1+1}=\frac{1}{3}{a_1}^2[/tex]

⇒ a2 = 1/3 (6)²

⇒ a2 = (1/3) × 36

⇒ a2 = 12

Substitute k = 2 in given recursive formula.

⇒ [tex]a_{2+1}=\frac{1}{3}{a_2}^2[/tex]

⇒ a3 = (1/3) × (12)²

⇒ a3 = (1/3) × 144

⇒ a3 = 48

Substitute k = 3 in given recursive formula.

⇒ [tex]a_{3+1}=\frac{1}{3}{a_3}^2[/tex]

⇒ a4 = (1/3) × (48)²

⇒ a4 = (1/3) × 2304

⇒ a4 = 768

Substitute k = 4 in given recursive formula.

⇒ [tex]a_{4+1}=\frac{1}{3}{a_4}^2[/tex]

⇒ a5 = (1/3) × (768)²

⇒ a5 = (1/3) × 589824

⇒ a5 = 196608

Therefore, the first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608

Learn more about the recursive formula of sequence here:

https://brainly.com/question/14457800

#SPJ4

Answer:

a) 20

Step-by-step explanation:

when we have an exponent of an exponent, we simply multiply them for the overall exponent.

so, we actually have

a^((1/4)×12) × b^((1/3)×12) = a³b⁴ = 5000

let's find the prime factors of 5000 :

5000 ÷ 2 = 2500

2500 ÷ 2 = 1250

1250 ÷ 2 = 625

625 ÷ 3 no

625 ÷ 5 = 125

125 ÷ 5 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

so,

5000 = 2³ × 5⁴

so, a = 2, b = 5

a²b = 2²×5 = 4×5 = 20

Using the distance between two points, it is found that you travel approximately 41 meters.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

In this problem, we have that:

Hence the distance is:

D = sqrt[(-15 - (-25))² + (15 - (-25))²] = sqrt(10² + 40²) = 41 meters.

More can be learned about the distance between two points at https://brainly.com/question/18345417

#SPJ1

The probability that the base-9 representation and the base-11 representation of are both three-digit numerals is 0.6753

To calculate the probability that the base-9 representation and the base-11 representation of are both three-digit numerals, we need the following parameters:

The smallest 3-digit base-11 number is 100

When converted to base 10, the equivalent number is 121

The largest 3-digit base-9 number is 888

When converted to base 10, the equivalent number is 728

So, the total number of possibilities is:

Possibilities = 728 - 121 + 1

Possibilities = 608

The count of base 10 3-digit numbers is

Count = 999 - 100 + 1

Count = 900

The required probability is:

P = 608/900

Evaluate

P = 0.6753

Hence, the probability that the base-9 representation and the base-11 representation of are both three-digit numerals is 0.6753

Read more about probability at:

https://brainly.com/question/24756209

#SPJ1

Complete question

A base-10 three-digit number is selected at random. What is the probability that the base-9 representation and the base-11 representation of are both three-digit numerals

Answer:

36

Step-by-step explanation:

don't know but let me check right quick

The size around the circular edge of the plate is 37.68 inches

The circumference of a circle can be solved as follows:

The ant is standing at the centre of a perfectly circular plate and it walks to the edge of the plate .

The centre of the plate to the edges is 6 inches. Therefore, the radius of the circular plate is 6 inches.

Hence, the distance around the edge of the plate is the circumference of the plate.

Therefore,

circumference of the circular plate = 2πr

circumference of the circular plate = 2 × π × 6

circumference of the circular plate = 12π

circumference of the circular plate = 12 × 3.14

circumference of the circular plate = 37.68 inches

learn more on circle here: https://brainly.com/question/9330354

#SPJ1

The correlation coefficient of r = 0.51 shows that it's an accurate value for this data.

A scenario that would be a causal relationship can be the quantity of fertilizer used vs kg of pumpkins picked on the farm

There is a correlation between the number of hours of sunlight that a plant receives and the height to which it grows.

The function that best fits the data is y = 3x + 4.

The y-intercept indicates that the plant started at 4cm and the slope shows that with each hour of sunlight, the plant grows 3 inches.

The association between two variables that are correlated can be shown by a scatter plot which has a trendline along which the data points are located.

A correlation coefficient of r = 0.51 is accurate based on the scatter plot given. If the trendline slopes upwards from the left to the right, it shows a positive correlation and vice versa.

A scenario that would be a causal relationship can be the quantity of fertilizer used vs kg of pumpkins picked on the farm.

There is a direct correlation between the number of hours of sunlight that a plant receives and the height to which it grows. This can be seen through the growth in the plant.

The function is y = 3x + 4

When x = 0, y = 3(0) + 4 = 4.

In conclusion, y-intercept indicates that the plant started at 4cm and the slope shows that with each hour of sunlight, the plant grows 3 inches.

Learn more about scatter plot on:

brainly.com/question/6592115

#SPJ1

To prove the similarity between the two circles we must translate circle A by <- 1, 1> and dilate the figure by a factor of 2.

Herein we must prove that two circles are similar by taking advantage of two key characteristics: (i) Center, (ii) Radius. Based on such facts, we must apply the following rigid transformation:

Step 1 - Traslating the circle from A to B: Translation vector - (- 1, 1).

(x, y) = (2, 3) + (- 1, 1)

(x, y) = (1, 4)

Step 2 - Dilate the circle by a factor of 2.

r = 2 · 5

r = 10

To prove the similarity between the two circles we must translate circle A by <- 1, 1> and dilate the figure by a factor of 2.

To learn more on transformation rules: https://brainly.com/question/9201867

#SPJ1

A graph which shows the image of ABCD is: A. on a coordinate plane, parallelogram A'B'C'D' has points (-2, 5), (0, 3), (0, -1.2), (-2, 1).

A transformation refers to the movement of a point on a cartesian coordinate from its original (initial) position to a new location.

In Geometry, there are different types of transformation and these include the following:

Based on transformation of parallelogram ABCD, we can infer and logically deduce that a graph which shows the image of ABCD is that on a coordinate plane, with parallelogram A'B'C'D' having points (-2, 5), (0, 3), (0, -1.2), (-2, 1) as shown in the image attached below.

Read more on transformations here: https://brainly.com/question/27939466

#SPJ1

Answer:  [tex]\\ \lim\limits_{k \to \infty} (1+\frac{4}{k})^k =e^4.[/tex]

Step-by-step explanation:

[tex]\displaystyle\\ \lim_{k \to \infty} (1+\frac{4}{k})^k \\x=\frac{x}{4} *4\\So,\ \lim_{k \to \infty} (1+\frac{4}{k})^\frac{k}{4}*4 \\ \lim_{k \to \infty} ((1+\frac{4}{k})^\frac{k}{4} )^4.\\Use\ the\ second\ wonderful\ limit:\\\boxed { \lim_{x \to \infty} (1+\frac{1}{x})^x=e },\\\\So,\\ \lim_{k \to \infty} (1+\frac{4}{k})^k =e^4.[/tex]

We can also apply l'Hôpital's rule by first rewriting the limit as

[tex]\displaystyle \lim_{k\to\infty} \left(1 + \frac4k\right)^k = \lim_{k\to\infty} \exp\left(\ln \left(1 + \frac4k\right)^k\right) = \exp\left(\lim_{k\to\infty} \frac{\ln\left(1+\frac4k\right)}{\frac1k}\right)[/tex]

Applying the rule gives

[tex]\displaystyle \lim_{k\to\infty} \frac{\ln\left(1+\frac4k\right)}{\frac1k} = \lim_{k\to\infty} \frac{\left(-\frac4{k^2}\right)/\left(1+\frac4k\right)}{-\frac1{k^2}} = 4 \lim_{k\to\infty} \frac1{1 + 4k} = 4[/tex]

so that the overall limit is

[tex]\displaystyle \lim_{k\to\infty} \left(1 + \frac4k\right)^k = \lim_{k\to\infty} \exp(4) = \boxed{e^4}[/tex]

Answer:

40 vanilla cookies

Step-by-step explanation:

Lets say that

N = No-bake cookies

V = Vanilla cookies

C = Cinnamon cookies

If the ratio is 2 : 2 : 2

And there are 40 no-bake cookies

It would be 40 vanilla cookies and 40 cinnamon cookies because the ratio is all the same

( N : V : C )

( 40 : 40 : 40 )

Hope this helps  (๑ > ᴗ <)وxx

( I am so sorry if this is wrong!!)

Answer: 4

Step-by-step explanation:

f(g(x)) = f(x+2) = 3(x+2) = 18

x + 2 = 6

x = 4

Answer:

x= 5 , for c to be same on each eqn

Answer:

Step-by-step explanation:

let the ratio of men women and children be 13x 5x and 7x

now

13x + 5x + 7x = 4152

25x = 4152

x = 4152/25

x = 166.08

The perimeter of the figure to the nearest tenth is 44.6 units

The perimeter of a figure is the sum of the whole sides.

Therefore,

A parallelogram has opposite sides equal to each other.

Therefore, the perimeter of the figure is as follows;

The figure combines a parallelogram and a semi circle.

Therefore,

perimeter of the figure = 4 + 14 + 14 + πr

perimeter of the figure = 32 + 3.14 × 4

perimeter of the figure = 32 + 12.56

perimeter of the figure = 44.56

perimeter of the figure ≈ 44.6 units

learn more on perimeter here: https://brainly.com/question/22532312

#SPJ1

Step-by-step explanation:

x = 7

y = 5

[tex] = {x}^{2} + {y}^{2} [/tex]

[tex] = (7 {)}^{2} + (5 {)}^{2} [/tex]

= 7 × 7 + 5 × 5

[tex] = 49 + 25 [/tex]

[tex] = 74[/tex]

Hey there!

x^2 + y^2

= 7^2 + 5^2

= 7 * 7 + 5 * 5

= 49 + 25

= 74

Therefore, your answer should be: 74

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The inequality sign < means "less than." If there is a line underneath the inequality sign that means "less than or equal to."

To graph x < 5, we first need to understand what the inequality is saying. In this case, x must be less than 5. So, a number that will make this inequality true will be less than, but not equal to, 5.

Start by putting an open circle on the number 5. An open circle indicates that 5 is not a value that works in this inequality. Then, we know that our values that make this inequality true are less than 5, so we'll draw an arrow from the circle to the left as numbers to the left of 5 are less than it.

Hope this helps!

The square root of the quantity x plus 7 end quantity minus 1 equals x=2.

To find the square root:

Check for extraneous solutions:

Therefore, the square root of the quantity x plus 7 end quantity minus 1 equals x = 2.

Know more about square roots here:

https://brainly.com/question/3617398

#SPJ4

The correct question is given below:
The square root of the quantity x plus 7 end quantity minus 1 equals x

Answer:

6 2 point shots 2 3 points

Step-by-step explanation:

3 two point shot 1 3 point shot = 9

6 two point shot 2 3 point shot =18

Answer:

x < -19/7

Step-by-step explanation:

Solve for x

2x+5  < (x+1)/4

Multiply each side by 4

4( 2x+5) <  (x+1)/4 *4

8x + 20  < x+1

Subtract x from each side

8x+20-x < x+1-x

7x + 20 < 1

Subtract 20 from each side

7x+20-20 < 1-20

7x< -19

Divide by 7

7x/7 < -19/7

x < -19/7

Answer:

[tex] \red{x < \frac{ - 19}{7} }[/tex]

Step-by-step explanation:

[tex]2x + 5 < \frac{x + 1}{4} \\ \text{use \: cross \: muliplication} \\ 4(2x + 5) < x + 1 \\ 8x + 20 < x + 1 \\ 8x - x < - 20 + 1 \\ 7x < - 19 \\ \frac{7x}{7} < \frac{ - 19}{7} \\ x < \frac{ - 19}{7} [/tex]

Answer:

(3, ∝) or all values of x greater than +3

Step-by-step explanation:

The inequality is [tex]5.5x + 15.5 > 32[/tex]

Subtracting 15.5 from both sides yields

5.5x > 32 - 15.5 or 5.5x > 16.5

Dividing by 5.5 on both sides yields

x > 16.5/5.5 or x > 3

This means the inequality is valid for all values of x > 3

The solution set is the interval (3, ∝ )

Answer:

Step-by-step explanation:

The equation of a circle in standard form is (x - h)² + (y - k)² = r² ,

where (h, r) are coordinates of a center of a circle and "r" is a radius of a circle.

a² ± 2ab + b² = (a ± b)²

~~~~~~~~~~

x² + y² - 2x - 10y + 17 = 0

To rewrite the equation in standard form, need to group terms with the same variables, move the constant to the right side and complete the square for each grouping:

(x² - 2x) + ( y² - 10y) = - 17

( x² - 2x + 1 ) + ( y² - 10y + 25 ) = - 17 + 1 + 25

( x - 1 )² + ( y - 5 )² = 9

( x - 1 )² + ( y - 5 )² = 3²

The center of the given circle is

( 1 , 5 )

The radius of the given circle is

3 units

the average pay per year is $4 million

Answer:

The average is 4millon

Step-by-step explanation:

because 16 millon divide by 4 =4

ez

The rotation of the triangle that's illustrated will be a rotation of 90°.

It should be noted that transformation is a general term for 4 specific ways that can be used to manipulate the shape and the position of a point, line, or a geometric figure. In such a case, the original shape of the object is called the pre-Image while the final shape and the position of the object is simply the image under transformation.

There are typically four common types of transformations and they're translation, rotation, reflection, as well as dilation. It should be noted that rotation about simply illustrates the transformation that takes place regarding the triangle.

For rotation, the shape rotates or turns the pre-image around the axis and there'll be no change in the size or shape of the object.

Here, the counterclockwise rotation was illustrated in the triangle ABC. Therefore, the rotation of the triangle that's illustrated will be a rotation of 90°.

In conclusion, based on the information given, the correct option is A.

Learn more about triangles on:

brainly.com/question/1058720

#SPJ1

Complete question:

Triangle ABCTriangle ABC is rotated to form △A'B'C' .

The coordinates of point A are (1, 1) , the coordinates of point B are (3, 1) , and the coordinates of point C are (1, 4) .

Which countr clockwise rotation around the origin results in the transformation of △ABC to △A'B'C' ?

Select from the drop down arrow to choose the correct rotation.

(a) rotation of 90

(b) rotation of 180

(c) rotation of 360