1: In his job as a cashier, Joe makes $500 each month plus $20 every time he convinces a customer to open a charge account at the store.

a. write the equation that describes Joe’s monthly income I as a function of n, the number of accounts that Joe solicits. Name the form of equation you wrote and why you chose to use that form.

b. This function is:
linear
exponential

c. This function is:
continuous
discrete

The volumes of the 20% solution, 35% solution, and 80% solution used by the chemist are 18 liters, 12 liters, and 24 liters, respectively.

The chemist has three different acidic solutions. The first solution contains 20% acid, the second contains 35% acid, and the third contains 80% acid. She created 54 liters of a 50% acid mixture, using all 3 solutions. The number of liters of 80% solution used is 2 times the number of liters of 35% solution used.

Let the amounts of 20% solution, 35% solution, and 80% solution used be x, y, and z. We already know that z = 2y. We can write equations as given below.

The sum of the volumes must be equal to the final volume.

x + y + z = 54

x + y + 2y = 54

x = 54 - 3y

Now we will write the equation using the concentrations of the acid.

50%*54 = 20%*x + 35%*y + 80%*z

27 = 0.2(54 - 3y) + 0.35y + 0.8(2y)

2700 = 20(54 - 3y) + 35y + 80(2y)

2700 = 1080 - 60y + 35y + 160y

1620 = 135y

y = 1620/135 = 12

z = 2y = 2*12 = 24

x = 54 - 3y = 54 - 36 = 18

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The value of the expression, 2w+4x, is 28 when w = 4 and x = 5.

According to the question,

We have the following expression:

2w+4x

We have the following values of w and x:

w = 4 and x = 5

Now, in order to find the value of the given expression, we will put these values in the expression.

So, we have this:

2*4+4*5

Now, we will first multiply the integers and then we will add the obtained results together:

8+20

28

Hence, the value of the expression, 2w+4x, is 28 when w = 4 and x = 5.

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Answer:

Step-by-step explanation:

You want the equation of the line with slope 3/5 that passes through point (5, 3).

The point-slope form of the equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

You have m=3/5, (h, k) = (5, 3), so your equation is ...

  y -3 = 3/5(x -5) . . . . point-slope form of desired equation

This can be simplified to ...

  y -3 = 3/5x -3

  y = 3/5x . . . . . . . add 3

the dimensions of the dumpster that will minimize its surface area

length l = 6.32

width w =  1.58

height h = 0.39

Length = l

width = w

height = h

given that length is four times its width

l = 4w

Now, the formula for the surface area of a cube is;

S = 2lh + 2lw + 2wh

substitute l = 4w in the above equation

S = 2(4w)h+2(4w)w+2wh

S = 8wh+8[tex]w^{2}[/tex]+2wh

S = 10wh + 8[tex]w^{2}[/tex]

formula for the volume of a cube is;

V = lwh

now substitute l=4w in the above equation

V = (4w)wh

V = 4[tex]w^{2}[/tex]h

h = 4[tex]w^{2}[/tex]/V

Put V/2w² for h in the surface area equation to get;

S= 8w² + 10w(V/4w²)

 = 8w² + 5V/2w

given that volume V = 25.6 substitute that in the above equation

S = 8w² + 5(25.6)/2w

  = 8w² + 128/2w

Since we want to minimize the surface area, let us find the first derivative of S to get;

S' = 16w - 128/2w²

At S' = 0

0 = 16w-  128/2w²

16w =  128/2w²

32w³ = 128

w³ = 128/32

w³ = 4

w = [tex]\sqrt[3]{4}[/tex]

w = 1.58 yds

since l = 4w substitute the value of w in that

l = 4(1.58) = 6.32

h = 4[tex]w^{2}[/tex]/V = 4([tex]1.58^{2}[/tex])/25.6

h = 0.39

the dimensions are

length l = 6.32

width w =  1.58

height h = 0.39

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The dividend growth rate of Kiefer service company is 0.16% . Dividend growth rate can be determined by using the return rate formula.

Dividend growth rate is the annual rate of growth that a particular stock's dividends experience over a specified period of time.

We have given that ,

Common stocks sells or current price = $36.84

Market rate of return (R) = 25.8 %

Annual dividend (D) = $1.61

Rate of return is defined as net gain or loss of। an investments over a specified time period . It is expressed as a percentage of investment initial cost .

Using the formula,

Rate of return = (D1/ current price )+growth rate where,

D1 --> divided of previous year

putting all the values in above formula we get,

15.8 = ( 1.61/36.84) + growth rate

=> growth rate= 15.8 - (1.61/36.84) = 15.756

Hense, the dividend growth rate for Kiefer service company is 0.16%.

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The only common factor (different than 1) between x and y is 29, so the greatest common divisor is 29.

Here we have two real numbers that are written as a product between their corresponding prime factors.

These numbers are:

x = 2*3*5*7*11*13*17*19*23*29

y = 29*31*37*41*43*47*53*59*61*67

Again, all of these are prime numbers, so the only common divisors between the two numbers are the factors that appear in both numbers.

And we can see that the only common factor between x and y is 29, then the greatest common divisor between x and y is 29.

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Answer:6400 multiplied  by 13% (0.13)  then multiply that answer by 52 , for weeks in the year.  

Step-by-step explanation:

6400*.013= $832.00

832*52= $43264.00

Step-by-step explanation:

The drawing has the side dimension of 7.6 cm

  since each cm represents 90 m   the ACTUAL park is

        7.6 x 90 = 684 meters

  similarly, the bottom of the drawing has the dimension 9.1 cm which represents    9.1 x 90 = 819 m

the area of the park is then

Area =  height x width =     684 m x 819 m = 560 196 m^2

OR  in one step:

Area of the actual park is then

(7.6 cm * 90 m / cm )   X  ( 9.1 cm * 90 m/cm ) = 560 196 m^2

Answer:

[tex]f(x) = (x+1)(x-2)(x+4)[/tex]

        [tex]= (x^{2} +x-2x-2)(x+4)\\\\= (x^{2} -x-2)(x+4)\\\\= x^{3}-x^{2}-2x+4x^{2} -4x-8\\\\= x^{3} +3x^{2} -6x-8[/tex]

The volume of a trunk of a regular quadrangular pyramid is 2754 cubic centimeters.

According to the question,

We have the following information:

The side of the base is 18cm, the length of the upper side is 7.5cm and the height of the trunk is 20.4cm.

Now, we know that the trunk of a regular quadrangular pyramid is in the shape of a cuboid.

And the following formula is used to find the volume of cuboid:

Length*breadth*height

​ Volume of a trunk of a regular quadrangular pyramid = 7.5*18*20.4

Volume of a trunk of a regular quadrangular pyramid = 2754 cubic centimeters

Hence, the volume of a trunk of a regular quadrangular pyramid is 2754 cubic centimeters.

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The greatest stress is experienced by object 2.

Stress is defined as force divided by area

Given: the table containing values of force and area for objects

Object 1

Stress = 72/6.46×10⁻⁵ =  1114551.084 N/m²

Object 2

Stress = 185/4.56×10⁻⁵ =  4057017.544 N/m²

Object 3

Stress = 406/5.07×10⁻⁴ =  792899.4083 N/m²

Object 4

Stress = 512/1.14×10⁻³ =  449122.807 N/m²

Therefore, object 2 is experiencing the greatest stress

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Answer:

Angle BAC =50

Step-by-step explanation:

Since O is the circumcenter and angle BOC is the angle subtended by the arc BC at the center and angle BAC is the angle subtended by arc BC

The range of the given function is represented as {y | -5 ≤ y ≤ 5 , y ∈ R} .

Range of a function is defined as the possible values of y or the dependent variable in relation to the values of x.

Here from the graph we can see that the greatest value y achieves is 5.

The lowest value of y from the graph is -5 for all the values of x.

Hence the range will be {-5 ≤ y ≤ 5}

Now the graph is continuous, so we accept all values of y, hence y ∈ R .

Therefore the range will be: {y | -5 ≤ y ≤ 5 , y ∈ R} .

The set of all possible values for the results of the dependent variable, or the entire set of all possible values when the domain is substituted, is the range of a function.

The steps to find the range is:

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Answer:

I think that the correct answers are C and D. I have questions. how many answers can I choose? what is the original photograph size? don't choose an answer until I get the information that I need

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{3}{5}}(x-\stackrel{x_1}{10}) \\\\\\ y-4=- \cfrac{3}{5}x+6\implies {\Large \begin{array}{llll} y=- \cfrac{3}{5}x+10 \end{array}}[/tex]

Answer:

4

Step-by-step explanation:

you can use the formula y=mx+b where b is 4

Mia's error in her thinking was that she interchanged the coordinate of both the x- and y-axis. Also, the point would actually be located at (5, 8).

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection across the x-axis is given by this transformation rule:

(x, y)                   →               (x, -y)

In Geometry, a reflection across the y-axis of a graph is given by this transformation rule (x, y) → (-x, y).

(x, y)                   →               (-x, y)

(-5, -8)                   →            (5, -8)

Next, we would apply another reflection across the x-axis of a graph as follows:

(x, y)                   →               (x, -y)

(5, -8)                   →            (5, 8)

In conclusion, we can logically deduce that Mia was wrong in her calculations.

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Answer: 5/6 windows in an hour, 6/5 hours, 72 minutes

Step-by-step explanation: the general formula used is 1/Oliver+1/sister=1/together and you plus in to find the amount of windows in an hour. Once solved, you take the reciprocal of that and that is the hours. Then you solve for the amount of minutes.

Answer:

x=9

Step-by-step explanation:

I assume you want me to solve for x.

6x+22=13x-41

Subtract 6x from both sides.

22=7x-41

Add 41 to both sides.

63=7x

Divide both sides by 7.

x=9.

CHECK:

6x+22=54+22=76

13x-41=117-41=76

76=76

So, x=9

Answer:

ones: 0

tenths: 9

thousandths: 3

Step-by-step explanation:

Because 0 is at the beginning of the whole "part" of the number, it is a "one" in place value (confusing right??) for example, in the number 54,743, 3 would be the digit in the ones place.

Because 9 is one decimal place across the example number, it is a tenth - because you would need 10 lots of 0.1 in order to make a whole number.

Because 3 is three decimal places across the example number, it is a thousandth - because you would need 1000 lots of 0.001 to make a whole number.

A good way of remembering these decimal place values is by using the number of zeros after 10, 100, 1,000, 10,000, and so on (one zero is a ten-th, two zeros is a hundred-th, etc, etc.)

The values of the variables "a", "b", and "c" are 3.06, 169.74, and 0, respectively. The total amount Gary will pay is $769.74.

Gary purchased a S750 TV on a credit card with a 22% annual percentage rate, and he wants to pay it off in payments of $200 per month. The table shows the information for the first four months after Gary used his credit card. We need to calculate the values of the missing variables and the total amount he will pay.

The variable "a" is the interest charged on the left amount in the third month.

a = (366.68 - 200)*0.018333 = 3.06

The variable "b" is the monthly amount paid by Gary. It is less than or equal to $200, depending on the payment amount. Since the amount to be paid is $169.74, which is less than $200, he will pay the whole amount in one go.

b = 169.74

The variable "c" is the interest charged on the left amount in the fourth month. Since then, the entire amount has been paid.

c = 0

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Answer:

the value of x is 135 i believe

Step-by-step explanation:

sorry if im wrong

Answer:

[tex]a_1=3[/tex]

[tex]a_n=a_n_-_1+2[/tex]

Step-by-step explanation:

Recursive formula : an = a(n-1) + d

where d = common difference , an = nth term, and n = number of terms

Because we are just writing the recursive formula rather than the explicit formula, the only defined term will be "d" or the common difference.

Here, the common difference is +2. This is evident as you must add 2 to get to 5 and then add 2 to get to 7 etc.

So d = 2

Plugging this into the recursive formula we get an = a(n-1) + 2

Also it's very important to state the first term which is 3 so a1 = 3

Solving an equation we will see that x = 13, then the measure of interior angle G is 63°.

Here we have the 3 interior angles of a triangle defined with a variable x.

m∠E = (5x + 6)°

m∠F = (4x - 6)°

m∠G = (5x - 2)°

Now, remember that the sum of the interior angles of a triangle is always equal to 180°.

Then we can write:

(5x + 6)° + (4x - 6)° +  (5x - 2)° = 180°

We can solve this for x.

14x - 2 = 180

14x = 180 + 2

x = 182/14 = 13

Now that we know the value of x, we can find the value of angle G.

m∠G = (5x - 2)° = (5*13 - 2)° = (15 - 2)° = 63°

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Answer:

1

3

6

are all the correct answers because they made the most sense and looked the most proportional

The length of the swimming pool is 30 feet

The width of the swimming pool is 15 feet

The volume of the swimming pool is 16875 gallons

Given,

Length of the rectangular swimming pool = 2x

Width of the rectangular swimming pool = x

A small concrete walkway surrounds the pool.

The width of the walkway = 2 feet

The area of the walkway = 196 square feet

We have to find the dimensions of the pool;

Here,

Area of rectangle = length x width

Area of walkways = (4x + 8x) + 4 x 4 = 196

12x + 16 = 196

12x = 196 - 16

12x = 180

x = 180/12

x = 15

That is,

Width of the pool is 15 feet

Length of the pool = 2 × x = 15 x 2 = 30 feet

Now,

If the depth of the pool is 6 feet, we have to find the amount of water that the pool can hold if the height of water is 1 foot below the top of the pool.

That is,

Volume of pool = length x width x depth

Here, depth = 6 - 1 = 5 feet

So,

Volume = 15 x 30 x 5 = 2250 cubic feet

Convert cubic feet to gallons

2250 x 7.5 = 16875 gallons of holding capacity

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The amount of chocolate left is three and seven-twelfths pounds

The amount of chocolate left is found by addition and subtraction of fraction

The fraction required are:

Eva bought seven and one-half pounds of chocolate chips = 7 1/2

She used three and three-fourths pounds = 3 3/4

two and five-sixths pounds in some muffins = 2 5/6

total amount used = addition of amount used

3 3/4 + 2 5/6

= 3 11/12

the amount left is gotten by subtraction of amount used from amount Eva bought

= 7 1/2 - 3 11/12

= 3 7/12

this is three seven-twelfths

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Approximately Carlo takes 2 minutes time to sing the song.

Given that, Ariel sings a song in 5.92 minutes. Carlos sings the same song in 7.73 minutes.

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

Now,

Difference of singing time = 7.73-5.92

= 1.81 minutes

≈ 2 minutes

Hence, approximately Carlo takes 2 minutes time to sing the song.

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Answer: y=-2x

Step-by-step explanation: Use the slope formula

-8-2/4-(-1)

-10/5=-2

y=-2

Answer:

y = - 2x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c  ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 2 ) and (x₂, y₂ ) = (4, - 8 )

m = [tex]\frac{-8-2}{4-(-1)}[/tex] = [tex]\frac{-10}{4+1}[/tex] = [tex]\frac{-10}{5}[/tex] = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 1, 2 )

2 = 2 + c ⇒ c = 2 - 2 = 0

y = - 2x + 0 , that is

y = - 2x ← equation of line