you are a bank teller, and your cash drawer
contains checks for $1,548.62, $321.05, $87.65, $245.10, $100.00, $32.22,
$12.32, $9.90, $4,598.00, $765.09, and $468.21. you have cash consisting
of 12 one hundred-dollar bills, 11 fifty-dollar bills, 31 twenty-dollar
bills, 17 ten-dollar bills, 45 five-dollar bills, and 36 one-dollar bills.
coins consist of 5 one-dollar pieces, 28 half dollars, 11 quarters, 22
dimes, 7 nickels, and 32 pennies. what is the total value of the drawer?

The required present ages of the father and the son are 47 years and 7 years respectively.

Let the present age of the father and the son be x years and y years, respectively.

According to the question,

Condition I,

2 years ago, the father's age was nine times the son's age.

or,(x−2)=9(y−2)

or,x−2=9y−18

or,x=9y−18+2

or,x=9y−16 - (i)

Condition II,

3 years later, the father's age will be five times the son's age.

or,(x+3)=5(y+3)

or,x+3=5y+15 - (ii)

Put the value of x from equation (i) in equation (ii), and we get,

or,(9y−16)+3=5y+15

or,9y−16=5y+15−3

or,9y−5y=12+16

or,4y=28

or,y=284

∴y=7

Put the value of y in equation (i), and we get,

or,x=9×7−16

or,x=63−16

∴x=47

So, (x,y) = (47,7)

Therefore, the required present ages of the father and the son are 47 years and 7 years respectively.

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Answer:

Step-by-step explanation:

it would be ch+24_438 of the data bewteen Ch bisect with angel DHG and MFG which is MOTHER of the angels

The power series representation for the function f(x) = x sin(4x) can be found as follows:

Firstly, we can find the power series representation of sin(4x) using the formula for the sine function:$

$\sin x = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}x^{2n+1}$$

Substitute 4x for x to obtain:$$\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}(4x)^{2n+1}

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+1}$$

Multiplying this power series by x gives:

$$x\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

Therefore, the power series representation for the function

f(x) = x sin(4x) is:$$f(x)

= x\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

Therefore, the power series representation for the function f(x) = x sin(4x) is:$$f(x) = x\sin 4x = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

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Answer:

  1435.5 m²

Step-by-step explanation:

You want the area of the triangular prism with base side lengths 12 m, 33 m, and 35 m, and height 13 m. The altitude of the base triangle is given as 11.3 m from the longest side.

The area of each triangular base is ...

  A = 1/2bh

  A = 1/2(35 m)(11.3 m) = 197.75 m²

The area of the three rectangular faces will be ...

  LA = (12 m)(13 m) +(33 m)(13 m) +(35 m)(13 m)

  = (13 m)(12 +33 +35 m) = (13 m)(80 m) = 1040 m²

The total area is the sum of the lateral area and the areas of the two bases:

  A = 1040 m² +2(197.75 m²) = 1435.5 m²

The surface area of the triangular prism is about 1435.5 m².

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The population of an island in 1950 was 2 million. The population grew exponentially for 63 years and reached 6.5 million in 2013. The carrying capacity of the island is estimated to be 10 million.

If the population growth rate in the future is similar to the last 50 years, what will the population be in 2050

The population is given to be increasing exponentially, which means it will follow the equation:

\($P(t) = P_0 e^{rt}$\)Here,\($P(t)$\) is the population after a period of time \($t$, $P_0$\) is the initial population, $r$ is the annual growth rate (which we are given is the same as the growth rate of the last 50 years), and \($t$\) is the time.

We can find the annual growth rate $r$ using the formula:\($$r = \frac{\ln{\frac{P(t)}{P_0}}}{t}$$\)
We know\($P_0 = 2$ million, $P(t) = 6.5$ million, and $t = 63$\) years. Substituting these values, we get:

\($r = \frac{\ln{\frac{6.5}{2}}}{63} = 0.032$\) (rounded to 3 decimal places)

Since the carrying capacity of the island is 10 million, we know that the population will not exceed this limit.

Therefore, we can use the logistic model to find the population growth over time. The logistic growth model is:

\($$\frac{dP}{dt} = r P \left(1 - \frac{P}{K}\right)$$\)

where $K$ is the carrying capacity of the environment. This can be solved to give:\($P(t) = \frac{K}{1 + A e^{-rt}}$\)

where \($A = \frac{K-P_0}{P_0}$. We know $K = 10$ million, $P_0 = 2$ million, and $r = 0.032$\). Substituting these values, we get:\($A = \frac{10-2}{2} = 4$\)

Therefore, the equation for the population of the island is:\($P(t) = \frac{10}{1 + 4 e^{-0.032t}}$\)

To find the population in 2050, we substitute\($t = 100$\) (since 63 years have already passed and we want to find the population in 2050, which is 100 years after 1950):

\($P(100) = \frac{10}{1 + 4 e^{-0.032 \times 100}} \approx \boxed{8.76}$ million\)
Therefore, the estimated population of the island in 2050, assuming constant carrying capacity and consumption per capita, is approximately 8.76 million.

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210 lbs is approximately equal to 95.2544 kg  ( rounded to four decimal places )

The conversion factor to convert lbs to kilogram is 0.453592

1 lbs = 0.453592 kg

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in kg = The mass in lbs × conversion factor

Substitute the values in the equation

1 lbs = 0.453592 kg

210 lbs = 210 × 0.453592

Multiply the numbers

= 95.2544 kg ( rounded to four decimal places )

Therefore, 210 lbs is 95.2544 kg

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Answer:

STAY SAFE STAY UGLY.

Step-by-step explanation:

BY ELON MUSK

The rule of translation for the given preimage and image will be (x, y) ⇒ (x - 2, x - 6). Then the correct option is A.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The coordinate of the preimage and image is given below.

A(2, -6) and A'(-4, -12)

The rule of transformation is given as,

(2, -6) = (- 4 - x, - 12 - y)

Compare the abscissa, then we have

2 = - 4 - x

x = -6

Compare the ordinate, then we have

- 6 = - 12 - y

y = -6

Then the rule of transformation is given as,

(x, y) ⇒ (x - 2, x - 6)

The standard of interpretation for the given preimage and picture will be (x, y) ⇒ (x - 2, x - 6). Then, at that point, the right choice is A.

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Answer:

eighty-nine point zero four

Step-by-step explanation:

Answer:

u mean 89.04 = eighty-nine point zero four?

Step-by-step explanation:

The required order for the three according to the turn of the audition is Heather, Jen, and bob.

Given that,
Jen, Heather, and Bob are auditioning for the same role. Jen auditions 10 minutes before four, Heather auditions 30 minutes before Jen, and Bob auditions 5 minutes before four. Order the three by who will audition first.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Let's order the timeline,

Jen's audition was 10 minutes before the 4, so the time is 3:50
Heather's audition was 30 minutes before so the time would be 3:20
Bob's audition was 5 minutes before the 4 so the time would be 3:55
So from the above calculation. the order of the audition is Heather, Jen, and bob.

Thus, the required order for the three according to the turn of the audition is Heather, Jen, and bob.

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Answer:

(3,7)

Step-by-step explanation:

Answer:

(x-3)^2-2

Step-by-step explanation:

Answer:

To rewrite the quadratic expression x^2 - 6x + 7 by completing the square, we need to follow these steps:

Take the coefficient of the x-term, which is -6, and divide it by 2. This gives us -3.

Square the result from step 1, which gives us 9.

Add and subtract the value obtained in step 2 to the quadratic expression, like this:

x^2 - 6x + 7 + 9 - 9

Group the first three terms and the last two terms separately and factor out the common factor from the first group:

(x^2 - 6x + 9) + (7 - 9)

Simplify the terms inside the brackets:

(x - 3)^2 - 2

Therefore, the expression x^2 - 6x + 7 can be rewritten as (x - 3)^2 - 2, which is in vertex form. The vertex of the parabola represented by this quadratic expression is (3, -2).

The product of 0.6 and 0.35 is 21/100.

To find the product of 0.6 and 0.35, we can multiply the whole numbers and then multiply the decimals separately.

Whole numbers:

0.6 can be expressed as 6/10

0.35 can be expressed as 35/100

Decimals:

0.6 × 0.35 = 6/10 × 35/100

Now let's calculate the product:

Whole numbers:

6 × 35 = 210

Decimals:

10 × 100 = 1000

The product of 0.6 and 0.35 is:

210/1000

Simplifying the fraction by dividing both numerator and denominator by their greatest common divisor (which is 10):

21/100

Therefore, the product of 0.6 and 0.35 is 21/100.

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Determine the conditions for when a function has an inverse. Use the horizontal line test to recognize when a function is one-to-one. Find the inverse of a given function.

It is simple to establish whether the inverse of a function is also a function using the horizontal line test.

Because it fails the vertical line test, a function's inverse might not actually be a function.

Graph of the line

f\left( x \right) = - x + 2

f(x)=−x+2.

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Step-by-step explanation:

given

\(f(x) = 3{(x + 1)}^{2} - 4 \\ f(3) = 3 {(3 + 1)}^{2} - 4 \\ = 3 {(4)}^{2} - 4 \\ = 3(16) - 4 \\ = 48 - 4 \\ = 44\)

Answer:

3(3+1)²-4

3(16)-4

48-4 = 44

The angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern is approximately 9.43 degrees

To find the angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern, we can use the concept of diffraction and the formula for the angle of the first minimum in a single-slit diffraction pattern:

sin(θ) = λ / (diameter)

where θ is the angle, λ is the wavelength of the sound, and the diameter is the diameter of the diaphragm.

First, let's convert the frequency of 15.69 kHz to the corresponding wavelength using the formula:

wavelength = speed of sound / frequency

wavelength = 1450 m/s / (15.69 kHz * 1000 Hz/kHz)

wavelength = 0.09257 meters (rounded to five decimal places)

Next, we can substitute the values into the formula to find the angle:

θ = \(sin^{(-1)}\) (0.09257 meters / 0.5806 meters)

θ ≈ 9.43 degrees (rounded to two decimal places)

Therefore, the angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern is approximately 9.43 degrees. This angle represents the bending or spreading of the sound waves as they pass through the circular hole of the diaphragm, creating the diffraction pattern.

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The economic impact of fishing for nearly all great lakes states varies, but according to a report by the U.S. Fish and Wildlife Service, it falls within the range of $1 to $8 billion (in millions of dollars).

This impact includes the economic contributions of recreational fishing, commercial fishing, and related industries such as tourism and boat manufacturing. The exact amount varies from state to state and from year to year depending on factors such as weather, fish populations, and fishing regulations.

The Great Lakes region of the United States is home to some of the largest freshwater bodies in the world and boasts a rich variety of fish species. Fishing is an important economic activity in the region, contributing billions of dollars to the local and national economy. The economic impact of fishing in the Great Lakes region includes not only the direct revenue generated by commercial and recreational fishing, but also the indirect and induced effects of fishing-related industries such as tourism and boat manufacturing.

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five out of of the twenty-five top-grossing films of 2017 in the united states were part of a movie franchise

If you were to attribute this film, that means you'd say that (something) caused the success of the movie Rocky. This question is basically asking what do you think made this movie a big hit? Personally, I'd say it's because of how the storyline and plot turned out. It's very intriguing and it doesn't just make the movie about boxing. The film adds some love between the protagonist and some other character, and not only that, but the movie teaches you something. Because Rocky lost to Apollo, Rocky didn't care. At least he still had Adrian. So, the movie teaches you that, even if you do lose, at least you still have something and/or someone with you.

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Answer:

Something that you can see to the human eye.

Answer:

visible is the capable of being seen

Answer:

0.33333

Step-by-step explanation:

Answer: the answer is 0.3 with a recipricol bar

Step-by-step explanation:

The six trigonometric functions has exact value with the given point on terminal side of an angle are,

sin θ = 7 / √53 , cos θ = 2 / √53 , tan θ = 7 / 2

cosec θ = √53 / 7 , sec θ = √53 / 2 , cot θ = 2 / 7

To determine the exact values of the six trigonometric functions ,

sine, cosine, tangent, cosecant, secant, and cotangent of an angle in standard position given a point on its terminal side,

Use the coordinates of the point.

Let's denote the angle as θ. The coordinates of the given point (2, 7) can be represented as (x, y) = (2, 7).

Using the Pythagorean theorem,  find the length of the hypotenuse of the right triangle formed by the given point and the origin (0, 0),

r = √(x² + y²)

= √(2² + 7²)

= √(4 + 49)

= √53

Now, determine the trigonometric functions using the definitions,

Sine

(sin θ) = y / r

          = 7 / √53

Cosine

(cos θ) = x / r

            = 2 / √53

Tangent

(tan θ) = y / x

          = 7 / 2

Cosecant

(cosec θ) = 1 / sin θ

                = √53 / 7

Secant

(sec θ) = 1 / cos θ

            = √53 / 2

Cotangent

(cot θ) = 1 / tan θ

           = 2 / 7

Therefore, the exact values of the six trigonometric functions of the angle are,

sin θ = 7 / √53

cos θ = 2 / √53

tan θ = 7 / 2

csc θ = √53 / 7

sec θ = √53 / 2

cot θ = 2 / 7

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Answer:

Step-by-step explanation:

The process of shaping has been used in the process to train the cat.

The shaping is the process or technique associated with rewarding to the animals or even humans. The method is commonly used to teach obedience and behaviour. It involves breaking down a specific task into small achievable and easy to do actions. It involves awarding on every step which gradually leads to the combination of overall task.

The example of cat here states giving treat at each step. The method was given by B. F. Skinner. Another characteristic of the method is teaching without physical control.

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The limit of the expression as x approaches -12 for x→−12 (√ (x^2 + 25) − 13) / (x + 12) exists and equals -4/5.

To evaluate the limit lim x→−12 (√(x^2+25)−13)/(x+12), we can try to directly substitute x=-12 into the expression. However, this results in an indeterminate form of 0/0, indicating that further algebraic manipulation is necessary.

One approach to evaluate this limit is to use algebraic manipulation to simplify the expression into a form that allows for direct substitution. To do this, we can multiply both the numerator and denominator by the conjugate of the numerator, which is √(x^2+25)+13. This results in the expression lim x→−12 (x^2 - 144) / (x+12)(√(x^2+25)+13).

We can then simplify the expression by factoring the numerator as (x-12)(x+12), canceling the (x+12) term in the numerator and denominator, and taking the limit as x approaches -12. This yields lim x→−12 (x-12)/(√(x^2+25)+13).

Substituting x=-12 into the simplified expression yields (-12-12)/(√(144+25)+13) = -24/30 = -4/5.

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The given problem is about a person named Priya who started with $50 in her bank account and deposited $20 each week for 12 weeks. We need to find out after how many weeks she will have $250 in her bank account and also plot the given data on a graph, given that technology is required.Let's solve the given problem step by step:a) We can represent Priya's bank account after n weeks as follows:$50 + $20n

This is because she started with $50 and deposited $20 each week for n weeks.Now, to graph this equation, we can use any graphing calculator or software.

For example, we can use the Desmos Graphing Calculator, which is free and available online.To plot the given data, we need to set the domain as {0, 1, 2, 3, ..., 12} (for 12 weeks), and the range as {50, 70, 90, 110, ..., 290} (according to the equation). Then we can plot the points as follows:

After plotting the points, we can connect them with a straight line to get the graph of the equation.$$$$b)

To mark the point that represents the amount after 3 weeks, we need to find the value of the equation for n = 3, which is:$50 + $20(3) = $110This means that after 3 weeks, Priya will have $110 in her bank account.

We can mark this point on the graph as follows:$$$$$c) To find out after how many weeks Priya will have $250 in her bank account, we need to solve the following equation:$50 + $20n = $250Subtracting $50 from both sides, we get:$20n = $200Dividing both sides by $20, we get:n = 10

This means that after 10 weeks, Priya will have $250 in her bank account. We can mark this point on the graph as follows:$$$$$Therefore,

we can conclude that it will take Priya 10 weeks to have $250 in her bank account, and we can represent this data on a graph using graphing technology.

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[a] Answer: y = 20x + 50

Step-by-step explanation:

    We can write a linear equation to answer this part. Priya starts with $50 and adds $20 every week. Let y be the total amount of money in the bank account and x be the number of weeks passed. We will write a slope-intercept equation, where 20 is the slope and 50 is the y-intercept.

    y = 20x + 50

[b] Answer: (3, 110)

Step-by-step explanation:

    Next, we will use a graphing calculator as asked. Here I am using Desmos Graphing Calculator, it is free to use and online. We can type in our equation above, y = 20x + 50. See attached. Since she will not have negative weeks that she deposits, and she only deposits for 12 weeks, we will add {0 ≤ x ≤ 12} to our equation when we graph.

    Since x is the number of weeks passed, 20(3) + 50 = 110, giving is the point (3, 110).

[c] Answer: 10 weeks

Step-by-step explanation:

    Now, we need to find the point where she has $250 in her bank account. Since y is the total amount of money in her bank account, we can find where y = 250 on the graph.

    This is at (10, 250), or 10 weeks.

5x^5/6

Step-by-step explanation:

Complete question :

A swimming pool is the shape of a right rectangular prism. If the pool is 12 3/4 yards long, 5 2/3 yards wide, and 9 yards deep, what is the volume of the swimming pool

Answer:

650 1/4 yd³

Step-by-step explanation:

Volume of a rectangle prism :

V = Length * width * height

V = 12 3/4 * 5 2/3 * 9

V = 51/4 * 17/3 * 9/1

V = (51*17*9) / (4*3*1)

V = 7803 / 12

V = 650 3/12

Volume of swimming pool = 650 1/4 yd³

The model "4 fraction bars. The fraction bars are labeled 1 and each have 6 boxes underneath labeled one-sixth" shows 4 divided by one-sixth = 24

The correct answer option is option A

Given:

4 fraction bars

If each fraction bars has 6 boxes, then, the total boxes for 4 fraction bars can be solved using ratio

1 fraction bars : 6 boxes

4 fraction bars : x

Equate the ratios

1 : 6 = 4 : x

1/6 = 4/x

cross product

1 × x = 4 × 6

x = 4 × 6/1

Divide by the reciprocal of 6/1

x = 4 ÷ 1/6

Hence the division problem that modelled the expression is 4 ÷ 1/6

4÷1/6 = 4×6/1

4÷1/6 = 24

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Step-by-step explanation:

You make a T-chart of x and y and graph it, like this:

If x = 1, y = 5

x   |    y

0   |   4

1    |   5

2   |   6

3   |   7

4   |   8

on and on it goes. . .